This document discusses different types of logical syllogisms:
1. Hypothetical syllogism uses a conditional premise and categorical conclusions. There are three types of hypothetical propositions: conditional, disjunctive, and conjunctive.
2. Conditional syllogism uses a conditional premise and its valid forms are modus ponens and modus tollens.
3. Disjunctive syllogism uses a disjunctive premise and its valid forms are ponendo tollens and tollendo ponens.
4. Conjunctive syllogism uses a conjunctive premise stating two choices cannot be true together.
It provides examples and
This document discusses different types of conditionals and their analysis. It begins by defining a conditional sentence as having an "if p then q" structure. Conditionals can be analyzed using possible worlds semantics similarly to modals.
The document then outlines four main uses of "if": standard conditionals which do not commit to the truth of the clauses but imply a relationship; relevance conditionals which commit to the truth of the consequent; factual conditionals which presuppose the antecedent is believed true; and concessive conditionals where the consequent is asserted regardless of the antecedent.
Finally, it distinguishes speech act conditionals, where the antecedent specifies when a speech act is fel
This document defines and explains logical concepts such as simple and compound statements, truth tables, logical operators like negation and conjunction, and argument validity. It discusses translating statements into symbolic logic using variables, determining statement truth values from truth tables, and classifying statements as tautologies, contradictions, or contingencies. Common valid argument forms like modus ponens and modus tollens are also defined.
Logical Operators in Brief with examplesMujtaBa Khan
This document defines and explains different types of logical operators: negation, conjunctions, disjunctions, conditionals, and bi-conditionals. It provides examples of each operator and includes their truth tables showing how the operators evaluate statements as true or false based on the truth values of the individual statements.
This document discusses various concepts in geometry including conditional statements, counterexamples, definitions, perpendicular lines, bi-conditional statements, deductive reasoning, the laws of logic, algebraic proofs using properties of equality, segment and angle properties, writing two-column proofs, the linear pair postulate, congruent and supplementary angle theorems, and the vertical angles theorem. Examples are provided to illustrate each concept.
- Abbreviated truth tables check an argument's validity by assuming the premises are true and conclusion is false, working backwards to assign true/false values to statements.
- For the argument "If A then B, A. Therefore B", assuming A is true and B is false leads to a contradiction, showing the argument is valid.
- More complex arguments may involve choices when multiple assignments could satisfy premises/conclusion. Finding a contradiction means that choice leads to a valid argument; an assignment without contradiction means the argument is invalid.
This document discusses deductive reasoning and conditional statements. It provides an example of a deductive argument about who committed a murder based on clues. The structure of the argument is analyzed by identifying the premises and conclusion. It also discusses the difference between deductive and inductive reasoning. Finally, it provides examples of conditional statements and identifies the hypothesis and conclusion in each.
Inductive reasoning uses examples and observations to reach a conclusion, called a conjecture. A conjecture is either always true or false. While examples can support a conjecture, they cannot prove it. A counterexample can demonstrate that a conjecture is false.
This document discusses different types of logical syllogisms:
1. Hypothetical syllogism uses a conditional premise and categorical conclusions. There are three types of hypothetical propositions: conditional, disjunctive, and conjunctive.
2. Conditional syllogism uses a conditional premise and its valid forms are modus ponens and modus tollens.
3. Disjunctive syllogism uses a disjunctive premise and its valid forms are ponendo tollens and tollendo ponens.
4. Conjunctive syllogism uses a conjunctive premise stating two choices cannot be true together.
It provides examples and
This document discusses different types of conditionals and their analysis. It begins by defining a conditional sentence as having an "if p then q" structure. Conditionals can be analyzed using possible worlds semantics similarly to modals.
The document then outlines four main uses of "if": standard conditionals which do not commit to the truth of the clauses but imply a relationship; relevance conditionals which commit to the truth of the consequent; factual conditionals which presuppose the antecedent is believed true; and concessive conditionals where the consequent is asserted regardless of the antecedent.
Finally, it distinguishes speech act conditionals, where the antecedent specifies when a speech act is fel
This document defines and explains logical concepts such as simple and compound statements, truth tables, logical operators like negation and conjunction, and argument validity. It discusses translating statements into symbolic logic using variables, determining statement truth values from truth tables, and classifying statements as tautologies, contradictions, or contingencies. Common valid argument forms like modus ponens and modus tollens are also defined.
Logical Operators in Brief with examplesMujtaBa Khan
This document defines and explains different types of logical operators: negation, conjunctions, disjunctions, conditionals, and bi-conditionals. It provides examples of each operator and includes their truth tables showing how the operators evaluate statements as true or false based on the truth values of the individual statements.
This document discusses various concepts in geometry including conditional statements, counterexamples, definitions, perpendicular lines, bi-conditional statements, deductive reasoning, the laws of logic, algebraic proofs using properties of equality, segment and angle properties, writing two-column proofs, the linear pair postulate, congruent and supplementary angle theorems, and the vertical angles theorem. Examples are provided to illustrate each concept.
- Abbreviated truth tables check an argument's validity by assuming the premises are true and conclusion is false, working backwards to assign true/false values to statements.
- For the argument "If A then B, A. Therefore B", assuming A is true and B is false leads to a contradiction, showing the argument is valid.
- More complex arguments may involve choices when multiple assignments could satisfy premises/conclusion. Finding a contradiction means that choice leads to a valid argument; an assignment without contradiction means the argument is invalid.
This document discusses deductive reasoning and conditional statements. It provides an example of a deductive argument about who committed a murder based on clues. The structure of the argument is analyzed by identifying the premises and conclusion. It also discusses the difference between deductive and inductive reasoning. Finally, it provides examples of conditional statements and identifies the hypothesis and conclusion in each.
Inductive reasoning uses examples and observations to reach a conclusion, called a conjecture. A conjecture is either always true or false. While examples can support a conjecture, they cannot prove it. A counterexample can demonstrate that a conjecture is false.
Against bounded-indefinite-extensibilityjamesstudd
This document discusses absolutism and relativism about quantifiers. It summarizes an argument by Dummett for relativism and considers two options for interpreting Dummett's use of "definite totality." Option 1, taking it to mean a set-like object, fails because the conclusion is not a threat to absolutism. Option 2, taking it to mean a "plurality," also fails because Dummett's premise is inconsistent in plural logic. The document then considers regimenting the paradoxes in a sorted logic to better state relativism and avoid trivial objections. It proposes treating interpretations as sequences and using auxiliary assumptions to formulate a paradox.
The document discusses various concepts in inductive and deductive reasoning including:
- Writing conjectures based on given information and finding examples/counterexamples
- Using Venn diagrams and truth tables to represent conjunctions, disjunctions, and conditionals
- The properties of conditionals including converse, inverse, and contrapositive
- Laws of logic like detachment and syllogism to make valid deductive arguments
- Postulates and properties related to geometry concepts like lines, planes, angles, and segments
The document discusses categorical propositions and their logical properties. It covers:
- The standard form of categorical propositions involving quantifiers like "all" and "some."
- The quality and quantity of propositions.
- Letter names assigned to proposition types.
- The distribution of terms and existential import of propositions.
- Systems for representing propositions diagrammatically, like Venn diagrams and the square of opposition.
- Conversions between propositions through operations like conversion, obversion, and contraposition.
- Testing proposition validity and logical fallacies from Boolean and Aristotelian perspectives.
The 180-degree rule establishes an imaginary line called the 'axis' that the camera cannot cross between a subject and the background to avoid disorienting the audience. Shot-reverse-shot is a common filming technique that alternates between two characters having a conversation. Match on action ensures continuity between cuts by keeping elements like positioning and actions the same.
Three uses for truth tables are:
1) To check if a sentence is tautological, contradictory, or contingent by examining if it is always true, always false, or can be either given different truth value assignments.
2) To check if two sentences are logically equivalent by seeing if they have the same truth value across all rows.
3) To check if an argument is valid by seeing if there is any row where the premises are all true and conclusion is false, which would mean the argument is invalid.
This document discusses logical connectives and truth functions. It explains that sentences can be combined using connectives like "and", "or", and "if...then..." to form longer sentences whose truth is determined by the truth values of the component sentences. Truth tables are used to represent the logical relationships between simple sentences and sentences connected by these logical operators. Key topics covered include conjunction, disjunction, negation, conditionals, biconditionals, and their associated truth tables.
Logical Connectives (w/ ampersands and arrows)dyeakel
This document introduces logical connectives and truth functions. It discusses the connectives "and", "or", "if...then...", and "if and only if" and provides their truth tables. Each connective takes truth values as input and determines a unique output value based on the inputs. For example, the truth table for "and" shows that a statement of the form "A and B" is true only when both A and B are true.
Here are the converses, inverses, and contrapositives of the given statements:
1. Conditional: If two angles form a linear pair, then they are supplementary.
Converse: If two angles are supplementary, then they form a linear pair.
Inverse: If two angles do not form a linear pair, then they are not supplementary.
Contrapositive: If two angles are not supplementary, then they do not form a linear pair.
2. Conditional: If a parallelogram has a right angle, then it is a rectangle.
Converse: If a parallelogram is a rectangle, then it has a right angle.
Inverse: If a parallelogram does not have
1) Categorical arguments are valid due to the relationship between categories, not individual sentences. Validity can be tested using Venn diagrams.
2) Venn diagrams represent categorical statements using circles to represent categories. Validity is determined by whether the conclusion is already contained within the representation of the premises.
3) Three-circle diagrams require representing statements carefully and checking if the conclusion is redundant given the premises.
This document provides information about trigonometric identities. It defines an identity as an equation that is true for all values of a variable, where the left and right sides are always equal. It then lists several common trigonometric identities, including reciprocal, quotient, Pythagorean, and even-odd identities. Examples are shown of establishing two identities by substituting known identities and simplifying until both sides are equal. Hints are provided for establishing identities, such as getting common denominators, using Pythagorean identities, and writing everything in terms of sines and cosines.
The document discusses the key concepts of logic, including the nature of arguments and their components. An argument consists of premises and a conclusion, which can be identified using common indicators. Deductive arguments claim necessity while inductive arguments claim probability. Valid deductive arguments cannot have true premises and a false conclusion, while strong inductive arguments make it improbable that the conclusion is false. The validity of an argument depends on its form.
An identity is a statement that two trigonometric expressions are equal for every value of the variable. Identities can be verified by manipulating one side of the equation using algebraic substitutions and trigonometric identities until it matches the other side, without moving terms across the equal sign. Practice is important to get better at verifying identities, as each one may require a different approach. Students should keep trying different methods and not get discouraged if it takes time to solve an identity.
The document summarizes key concepts in geometry including conditional statements, counter-examples, definitions, bi-conditionals, deductive reasoning, laws of logic, algebraic proofs, segment and angle properties, two-column proofs, the linear pair postulate, congruent complement and supplement theorems, the vertical angles theorem, and the common segments theorem. Examples are provided for each concept.
This document summarizes an algorithm lecture about stable matchings. It introduces the stable matching problem and Hall's marriage theorem. It then describes Gale-Shapley's stable matching algorithm, where men and women rank their preferences and men iteratively propose to the highest ranked remaining women. The algorithm is proven to always terminate with a stable matching in polynomial time.
This document provides guidance on establishing trigonometric identities by substituting known identities and simplifying expressions until both sides of the equality are equivalent. It reviews basic reciprocal, quotient, and Pythagorean identities that can be used. Tips are given such as working with the more complex side first, multiplying the numerator and denominator by conjugates, and writing all expressions in terms of sines and cosines if needed. The goal is to use identities and algebra to prove two expressions are equal without moving terms across the equal sign.
This document discusses logical connectives and truth functions. There are five basic connectives: conjunction, disjunction, negation, implication, and equivalence. Truth functions combine sentences in ways that the truth value of the longer sentence is determined by the truth values of the parts. Each connective is represented by a symbol and has a corresponding truth table that shows the possible truth value combinations of the statements joined by the connective.
This document proposes a modal logic called NL that can analyze common language sentences while avoiding paradoxes. NL refines the law of excluded middle so it only applies when a sentence is not self-contradictory. This allows sentences like "this statement is false" to be considered false without violating classical logic. NL also includes new axioms like Then-4 that allow for paradox-causing sentences to be deemed false. The goal is for NL to have many of the useful properties of classical logic while properly handling paradoxes in natural language.
This document provides an introduction to propositional logic and first-order logic. It defines propositional logic, including propositional variables, connectives like conjunction and disjunction, and the laws of propositional logic. It then introduces first-order logic, which adds quantifiers, variables, functions, and predicates to represent objects, properties, and relations in a domain. First-order logic allows for more expressive statements about individuals and generalizations than propositional logic alone.
The document discusses deductive and inductive arguments. It provides examples of valid and invalid deductive arguments using categorical propositions and conditional premises. It also discusses inductive arguments, noting that inductive conclusions generalize from specific premises rather than necessarily following from them. The document then compares deductive and inductive arguments and discusses their uses in everyday life and mathematics. It concludes by introducing some common rules of inference for deductive arguments.
The document discusses logical concepts such as meaning, truth, negation, and logical relations between sentences and words. It provides examples to illustrate key logical principles like the principle of polarity, which states that a sentence is either true or false; negation, where negating a sentence reverses its truth value; and logical relations like entailment, equivalence, contradiction, and independence. Logical relations depend on the truth conditions of sentences rather than their literal meanings. Predicate terms can have logical relations like equivalence if they have the same denotation, and subordination if one term is true of arguments whenever another term is true of them.
The document discusses the constraint satisfaction problem (CSP) and the dichotomy conjecture regarding the complexity of CSP instances. It provides definitions and examples of CSPs. It explains the role of polymorphisms in determining the complexity, identifying semilattice, majority and affine polymorphisms as "good". It outlines the dichotomy conjecture that CSPs are either solvable in polynomial time or NP-complete depending on the presence of certain types of local structure defined by polymorphisms. The document also discusses algorithms and results for various constraint languages.
The document provides an introduction to formal logic. It discusses how to formulate valid arguments through propositional logic and syllogistic logic. Propositional logic uses truth tables to evaluate combinations of propositions and operators like negation and conjunction. Syllogistic logic examines implications of general statements using domains and categories. The key rules of inference for valid arguments are hypothetical syllogism, modus ponens, and modus tollens.
Against bounded-indefinite-extensibilityjamesstudd
This document discusses absolutism and relativism about quantifiers. It summarizes an argument by Dummett for relativism and considers two options for interpreting Dummett's use of "definite totality." Option 1, taking it to mean a set-like object, fails because the conclusion is not a threat to absolutism. Option 2, taking it to mean a "plurality," also fails because Dummett's premise is inconsistent in plural logic. The document then considers regimenting the paradoxes in a sorted logic to better state relativism and avoid trivial objections. It proposes treating interpretations as sequences and using auxiliary assumptions to formulate a paradox.
The document discusses various concepts in inductive and deductive reasoning including:
- Writing conjectures based on given information and finding examples/counterexamples
- Using Venn diagrams and truth tables to represent conjunctions, disjunctions, and conditionals
- The properties of conditionals including converse, inverse, and contrapositive
- Laws of logic like detachment and syllogism to make valid deductive arguments
- Postulates and properties related to geometry concepts like lines, planes, angles, and segments
The document discusses categorical propositions and their logical properties. It covers:
- The standard form of categorical propositions involving quantifiers like "all" and "some."
- The quality and quantity of propositions.
- Letter names assigned to proposition types.
- The distribution of terms and existential import of propositions.
- Systems for representing propositions diagrammatically, like Venn diagrams and the square of opposition.
- Conversions between propositions through operations like conversion, obversion, and contraposition.
- Testing proposition validity and logical fallacies from Boolean and Aristotelian perspectives.
The 180-degree rule establishes an imaginary line called the 'axis' that the camera cannot cross between a subject and the background to avoid disorienting the audience. Shot-reverse-shot is a common filming technique that alternates between two characters having a conversation. Match on action ensures continuity between cuts by keeping elements like positioning and actions the same.
Three uses for truth tables are:
1) To check if a sentence is tautological, contradictory, or contingent by examining if it is always true, always false, or can be either given different truth value assignments.
2) To check if two sentences are logically equivalent by seeing if they have the same truth value across all rows.
3) To check if an argument is valid by seeing if there is any row where the premises are all true and conclusion is false, which would mean the argument is invalid.
This document discusses logical connectives and truth functions. It explains that sentences can be combined using connectives like "and", "or", and "if...then..." to form longer sentences whose truth is determined by the truth values of the component sentences. Truth tables are used to represent the logical relationships between simple sentences and sentences connected by these logical operators. Key topics covered include conjunction, disjunction, negation, conditionals, biconditionals, and their associated truth tables.
Logical Connectives (w/ ampersands and arrows)dyeakel
This document introduces logical connectives and truth functions. It discusses the connectives "and", "or", "if...then...", and "if and only if" and provides their truth tables. Each connective takes truth values as input and determines a unique output value based on the inputs. For example, the truth table for "and" shows that a statement of the form "A and B" is true only when both A and B are true.
Here are the converses, inverses, and contrapositives of the given statements:
1. Conditional: If two angles form a linear pair, then they are supplementary.
Converse: If two angles are supplementary, then they form a linear pair.
Inverse: If two angles do not form a linear pair, then they are not supplementary.
Contrapositive: If two angles are not supplementary, then they do not form a linear pair.
2. Conditional: If a parallelogram has a right angle, then it is a rectangle.
Converse: If a parallelogram is a rectangle, then it has a right angle.
Inverse: If a parallelogram does not have
1) Categorical arguments are valid due to the relationship between categories, not individual sentences. Validity can be tested using Venn diagrams.
2) Venn diagrams represent categorical statements using circles to represent categories. Validity is determined by whether the conclusion is already contained within the representation of the premises.
3) Three-circle diagrams require representing statements carefully and checking if the conclusion is redundant given the premises.
This document provides information about trigonometric identities. It defines an identity as an equation that is true for all values of a variable, where the left and right sides are always equal. It then lists several common trigonometric identities, including reciprocal, quotient, Pythagorean, and even-odd identities. Examples are shown of establishing two identities by substituting known identities and simplifying until both sides are equal. Hints are provided for establishing identities, such as getting common denominators, using Pythagorean identities, and writing everything in terms of sines and cosines.
The document discusses the key concepts of logic, including the nature of arguments and their components. An argument consists of premises and a conclusion, which can be identified using common indicators. Deductive arguments claim necessity while inductive arguments claim probability. Valid deductive arguments cannot have true premises and a false conclusion, while strong inductive arguments make it improbable that the conclusion is false. The validity of an argument depends on its form.
An identity is a statement that two trigonometric expressions are equal for every value of the variable. Identities can be verified by manipulating one side of the equation using algebraic substitutions and trigonometric identities until it matches the other side, without moving terms across the equal sign. Practice is important to get better at verifying identities, as each one may require a different approach. Students should keep trying different methods and not get discouraged if it takes time to solve an identity.
The document summarizes key concepts in geometry including conditional statements, counter-examples, definitions, bi-conditionals, deductive reasoning, laws of logic, algebraic proofs, segment and angle properties, two-column proofs, the linear pair postulate, congruent complement and supplement theorems, the vertical angles theorem, and the common segments theorem. Examples are provided for each concept.
This document summarizes an algorithm lecture about stable matchings. It introduces the stable matching problem and Hall's marriage theorem. It then describes Gale-Shapley's stable matching algorithm, where men and women rank their preferences and men iteratively propose to the highest ranked remaining women. The algorithm is proven to always terminate with a stable matching in polynomial time.
This document provides guidance on establishing trigonometric identities by substituting known identities and simplifying expressions until both sides of the equality are equivalent. It reviews basic reciprocal, quotient, and Pythagorean identities that can be used. Tips are given such as working with the more complex side first, multiplying the numerator and denominator by conjugates, and writing all expressions in terms of sines and cosines if needed. The goal is to use identities and algebra to prove two expressions are equal without moving terms across the equal sign.
This document discusses logical connectives and truth functions. There are five basic connectives: conjunction, disjunction, negation, implication, and equivalence. Truth functions combine sentences in ways that the truth value of the longer sentence is determined by the truth values of the parts. Each connective is represented by a symbol and has a corresponding truth table that shows the possible truth value combinations of the statements joined by the connective.
This document proposes a modal logic called NL that can analyze common language sentences while avoiding paradoxes. NL refines the law of excluded middle so it only applies when a sentence is not self-contradictory. This allows sentences like "this statement is false" to be considered false without violating classical logic. NL also includes new axioms like Then-4 that allow for paradox-causing sentences to be deemed false. The goal is for NL to have many of the useful properties of classical logic while properly handling paradoxes in natural language.
This document provides an introduction to propositional logic and first-order logic. It defines propositional logic, including propositional variables, connectives like conjunction and disjunction, and the laws of propositional logic. It then introduces first-order logic, which adds quantifiers, variables, functions, and predicates to represent objects, properties, and relations in a domain. First-order logic allows for more expressive statements about individuals and generalizations than propositional logic alone.
The document discusses deductive and inductive arguments. It provides examples of valid and invalid deductive arguments using categorical propositions and conditional premises. It also discusses inductive arguments, noting that inductive conclusions generalize from specific premises rather than necessarily following from them. The document then compares deductive and inductive arguments and discusses their uses in everyday life and mathematics. It concludes by introducing some common rules of inference for deductive arguments.
The document discusses logical concepts such as meaning, truth, negation, and logical relations between sentences and words. It provides examples to illustrate key logical principles like the principle of polarity, which states that a sentence is either true or false; negation, where negating a sentence reverses its truth value; and logical relations like entailment, equivalence, contradiction, and independence. Logical relations depend on the truth conditions of sentences rather than their literal meanings. Predicate terms can have logical relations like equivalence if they have the same denotation, and subordination if one term is true of arguments whenever another term is true of them.
The document discusses the constraint satisfaction problem (CSP) and the dichotomy conjecture regarding the complexity of CSP instances. It provides definitions and examples of CSPs. It explains the role of polymorphisms in determining the complexity, identifying semilattice, majority and affine polymorphisms as "good". It outlines the dichotomy conjecture that CSPs are either solvable in polynomial time or NP-complete depending on the presence of certain types of local structure defined by polymorphisms. The document also discusses algorithms and results for various constraint languages.
The document provides an introduction to formal logic. It discusses how to formulate valid arguments through propositional logic and syllogistic logic. Propositional logic uses truth tables to evaluate combinations of propositions and operators like negation and conjunction. Syllogistic logic examines implications of general statements using domains and categories. The key rules of inference for valid arguments are hypothetical syllogism, modus ponens, and modus tollens.
The document discusses the constraint satisfaction problem (CSP) and the dichotomy conjecture in computational complexity theory. It defines CSP and provides examples. It discusses the role of polymorphisms - operations that preserve constraints. The presence or absence of certain polymorphisms like semilattice, majority, and affine operations determines the complexity of CSP for a given constraint language. The document outlines a proposed dichotomy - CSP is either solvable in polynomial time or NP-complete, depending on the polymorphisms. It surveys partial results proving this conjecture and algorithms for certain constraint languages.
Prof. Rob Leight (University of Illinois) TITLE: Born Reciprocity and the Nat...Rene Kotze
This document discusses Born reciprocity in string theory and how it relates to the nature of spacetime. It argues that while string theory is formulated in terms of maps into spacetime, this breaks Born reciprocity. The document suggests that quasi-periodicity of strings without assuming a periodic target spacetime better respects Born reciprocity. This leads to a phase space formulation of string theory without assuming locality of spacetime at short distances.
This document discusses Born reciprocity in string theory and how it relates to the nature of spacetime. It argues that while string theory is formulated in terms of maps into spacetime, this breaks Born reciprocity. The document suggests that quasi-periodicity of strings without assuming a periodic target spacetime better respects Born reciprocity. This leads to a phase space formulation of string theory without assuming locality of spacetime at short distances.
This document provides an overview of propositional logic including:
- The basic components of propositional logic like propositions, connectives, truth tables
- Applications such as translating English sentences to logic, system specifications, puzzles
- Logical equivalences and showing equivalence through truth tables
- Sections cover propositions, connectives, truth tables, and applications including translation, specifications, puzzles
It was Kepler who first asked whether contra-globally bounded homomorphisms can be classified. Hence unfortunately, we cannot assume that M is differentiable and pointwise generic. Therefore this reduces the results of [9] to a well-known result of Sylvester [32, 21]. Now it would be interesting to apply the techniques of [31] to associative, naturally Euclid elements. Thus a central problem in elliptic calculus is the derivation of countable monoids.
This document summarizes Chapter 1, Part I of a textbook on propositional logic. It introduces key concepts in propositional logic, including propositions, logical connectives like negation, conjunction, disjunction, implication, biconditional, and truth tables. It provides examples of applying propositional logic to represent English sentences, system specifications, logic puzzles and logic circuits. It also briefly describes representing knowledge about an electrical system in propositional logic for fault diagnosis in artificial intelligence.
A Unifying theory for blockchain and AILonghow Lam
This document proposes a unifying theory connecting blockchain and artificial intelligence technologies. It introduces the Lam-Visser theory and how it fits within the Damhof Quadrants framework. The document provides definitions related to the main result, which states that there exists a minimal, ultra-connected, almost everywhere linear and generic solvable, semi-countable polytope if a certain condition is met. It then discusses applications of this theory to questions of associativity and the computation of analytically independent subalgebras.
A smooth-exit the-phase-transition-to-slow-roll-eternal-inflationmirgytoo
This document summarizes research on the phase transition to eternal inflation. It begins by introducing the concept of eternal inflation occurring when quantum fluctuations dominate over classical drift. The authors argue that even in the eternal inflation regime, perturbations of the geometry and interactions remain perturbative, allowing quantitative analysis. They aim to precisely define the critical condition for eternal inflation and calculate statistics of the reheating volume to understand the phase transition.
Discrete math is the branch of mathematics that does not rely on limits. It is well-suited to describe computer science concepts precisely as computers operate discretely in discrete steps. The document provides an overview of topics in discrete math including logic, sets, proofs, counting, and graph theory. These topics provide the tools needed for creating and analyzing sophisticated algorithms.
Similar to Fuzziness and the sorites paradox. Summary of Chapter 1 and 6 (17)
La Unión Europea ha acordado un paquete de sanciones contra Rusia por su invasión de Ucrania. Las sanciones incluyen restricciones a los bancos rusos, la prohibición de exportaciones de alta tecnología a Rusia y la congelación de activos de oligarcas rusos. Los líderes de la UE esperan que estas medidas disuadan a Rusia de continuar su agresión militar contra Ucrania.
Este documento resume la evolución histórica del reconocimiento de los derechos humanos según el pensamiento de Lorenzo Peña. Comienza con los derechos reconocidos en la antigüedad como derechos civiles, políticos y de bienestar. Luego describe el desarrollo de los derechos a lo largo de la Edad Media y la Edad Moderna, incluyendo el surgimiento del contractualismo. Finalmente, analiza el reconocimiento constitucional de los derechos naturales y de bienestar en documentos como la Declaración de los Dere
Este documento presenta un vocabulario básico de latín elaborado por María Patricia Valverde Vásquez para la Universidad de Cuenca. El vocabulario fue editado por Marcelo Vásconez Carrasco e incluye palabras latinas comunes con sus traducciones al español. Se basa en dos fuentes principales y agradece a Patricia Valverde por compilar el vocabulario.
Tabla de posiciones en la filosofía política con respecto a las funciones del Estado, con sus bases en la la axiología (valores) y la ética (derechos y deberes).
Brevísima panorámica histórica del surgimiento y evolución de los derechos humanos, desde la Antigüedad hasta el s. XX, con énfasis en su fundamentación (discusión entre jusnaturalismo y juspositivismo), la correlación entre derechos y deberes,
Este documento presenta un análisis crítico de si el Estado debe garantizar el bienestar colectivo desde una perspectiva ética política. Explora esta pregunta central a través de preguntas subsidiarias y clasifica las posiciones de varios autores entre anarquismo, libertarismo, marxismo, liberalismo y otros enfoques. El objetivo es debatir esta cuestión compleja con ideas extraídas de diferentes corrientes de pensamiento político.
Este documento discute la posición jusnaturalista de los derechos humanos según Lorenzo Peña. Se argumenta que los derechos se derivan de la necesidad de participar en el bien común y de la pertenencia a la especie humana. Esto implica que los derechos fundamentales limitan la propiedad privada y justifican la intervención estatal para garantizar el bienestar cuando la empresa privada no provee servicios accesibles.
El documento presenta el programa del I Congreso de Ética y Filosofía Política que se llevará a cabo del 23 al 25 de junio de 2014 en la Universidad de Cuenca. El congreso contará con paneles y presentaciones sobre temas como el buen vivir, la educación, la ética, el poder, la utopía, la historia, el socialismo del siglo XXI y la Revolución Ciudadana. Los objetivos del congreso son brindar un espacio para la discusión de investigaciones sobre ética y filosofía política, reflexionar sobre prop
Este documento presenta una discusión sobre las teorías éticas del bien y el deber. Resume las posiciones del hedonismo, que sostiene que el placer es el único bien intrínseco, y del pluralismo, que argumenta que hay múltiples bienes intrínsecos como el conocimiento y la virtud. También compara las teorías consecuencialistas del deber, como el utilitarismo, que juzga las acciones por sus consecuencias, con las teorías antecedentalistas, que evalúan la intención detrás de las acciones.
Este documento describe una técnica de lectura con subrayado multicolor para resaltar diferentes tipos de información en un texto filosófico, como planteamientos de problemas, definiciones, opiniones de otros autores, conclusiones y recomendaciones. Se recomienda asignar un color diferente a cada tipo de contenido para facilitar la búsqueda de información. Al subrayar, se sugiere marcar las ideas más importantes con líneas verticales, corchetes o subrayados completos, dependiendo de su nivel de importancia, para minimizar la cantidad de subrayado
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Fuzziness and the sorites paradox. Summary of Chapter 1 and 6
1. Fuzziness and the Sorites Paradox
by Marcelo Vásconez
Chapter 1: Introduction
1b Principles of Bivalence. Sensu stricto: T and F jointly exhaustive and mutually exclusive. Rejected.
Loose sense: "p" is true or false. Accepted.
1c Principles of Excluded Middle: Strong: (3) "pw¬p" true, to some degree however small.
Absolute: (4) "H(pw~p)", (5) "Hpw¬p" both totally false.
Weak or simple: (1) "pw~p" at least 50% true, and at most 50% false. (2) "Lpw¬p" completely true.
FUZZINESS
3bi Fuzzy fact: (6) ~(ΔφxwΔ~φx) = (5) ~Δφxv~Δ~φx ± (8) ~Hφxv~¬φx ˆ (1) ~φxv~~φx
Softly indeterminate.
Fuzziness weakly falsifies the simple PEM & vice versa. However, we can have both.
Absolute PEM: (9) ΔφxwΔ~φx = (11) Hφxw¬φx completely incompatible with (6)
Inverse Co-variance of Opposites (ICO): the more φ x is, the less ~φ it is ± › no total indetermination
3bii Borderline case is contradictory: (13) ~φxvφx, from (1) of 3bi + DN.
Border zone instead of border line. Not all borderline cases are equally distanced from the extremes.
3biii Fuzzy property has many borders. x is <φ than y ± x is >-φ than y ± x is -φ.
There is a soft limit whenever there is a relation of inferiority, because of the ICO, and the:
Aristotelian Rule for Comparatives: possession of φ in a > or < degree implies unqualified possession.
Paraconsistent soft borders: there are φ things on both sides of the border.
3biv Fuzziness generates the sorites, but is not responsible for the absurdity.
SORITES
4b Intuitive Major Premise: The loss of a single hair cannot turn a hairy man bald.
Ψ-φ Correspondence Principle: no tiny alteration in Ψ creates a significant change in φ
Major Premise extends the status of a0 to all other ai. Against transition from φ to not-φ.
What is fuzzy diffuses itself.
4d Soritical Series. Core idea: ai and ai+1 almost completely similar with minimal dissimilarity;
subjectively indiscernible. How to capture this logically?
(SP) φai vφai+1w.~φai v~φai+1 ± (CP) ~(φai v~φai+1) = (Par.P.) ~φai wφai+1
The Fairness Principle: Like cases must be treated alike.
(Pre.P) φaieφai+1. Completely false for the last two members, in bounded series.
It does not represent the relation of contiguous members in a soritical series.
We must render the Major Premise in terms of disjunction + weak negation. Rule: DS.
5 Denials of Major Premise. Discontinuism: (DT): ›ai, ai+1(Hφaiv¬φai+1). Sharp boundary
Criticisms: To deny the intuitive major premise is empirically false.
To deny (Ψ-φ C) goes against common sense truisms, backed up by paraconsistency.
DT is arbitrary, against likeness of adjacent members, and unfair: it discriminates indiscriminable cases.
However, no major premise is completely true, for they all are partially false.
There is a soft boundary: ›ai, ai+1(φaiv~φai+1)
DS is invalid for the weak negation, though valid for the strong negation.
6 The Rejection of the Slippery Slope. If the RI (transitivity of the closeness relation) fails, then:
Maximalism: in order for x to be φ, it is necessary that x be absolutely φ.
Only prototypes. What is good? The optimum.
Alethic Maximalism: a sentence is true only if totally true.
Criticisms: 1) Massive impoverishment of reality. Deficient instances eliminated. Fuzziness abolished.
2) No degrees, and no comparatives.
When the property is unbounded, accept the conclusion of the slippery slope: everything is φ.
2. Summary of Ch. 6: “Contradictorial Gradualism vs. Discontinuism”
2. The Soritical Series. Easy cases: two extremes + every pair so very much alike that:
(CP) Continuation Principle: -(Fai v -Fai+1), or
(SP) Similarity Principle: Fai v Fai+1 w. -Fai v -Fai+1.
N.B. Both principles are formulated with weak negation. Invalid for strong negation, ‘¬’.
3. Nature & Cause of the Transition. Our point of departure: occurrence of a soritical transition.
Q1: What is the nature of the transition? Gradual or abrupt?
Q2: Why does the transition happen? What is its condition of possibility?
4. Is the Transition Possible? If (CP) prohibits a dividing line, how the transition is possible?
If there is a transition ± contradiction: a50 is F and not F, by (SP).
Prima facie incompatibility between the soritical series and the transition.
5. Nihilism. There is no transition.
ASSESSMENT. Nihilism offers no positive clarification, no constructive account of Q1, nor of Q2.
6a. Discontinuism and Abrupt Transition. CP is false. The soritical series is impossible. Then,
(DT) Discontinuity Thesis: ›ai (Fai v ¬Fai+1).
There is a sharp cut-off point. a1 bipartitions the series ± there are no proper borderline cases.
Tertium non datur.
Answer to Q1: sudden transition. Punctual. Death is instantaneous. Change would not be continuous.
ASSESSMENT. Unacceptable dualism for its inadmissible consequences.
Change reduced to a precipitous replacement of two stages.
Transitions are contradictory. Example: walking out of the room.
Reductio ad absurdum not valid for weak negation.
6b. ...and the Cause of Change. Answer to Q2: Passage from ai to ai+1 accounts for the transition.
ASSESSMENT. Not every alteration in the underlying dimension G produces changes in F.
There is lack of proportional correspondence between changes in G and changes in F/not F.
Small quantitative changes in G might produce large changes in the supervening F.
Minimal change in G (losing one hair) does not explain drastic change in F (becoming bald).
Why change? There is no principled ground. Point ai is arbitrary. Enigmatic transition.
7. Contradictorial Gradualism (Lorenzo Peña)
7a. Fuzziness = intermediate zone between the extremes –if any– of the soritical series.
Gradual & Contradictory. Not homogeneous: different proportions of F and not F.
7b. Degrees of Properties. 1) Ancients formulated problem in gradual terms. Little by little.
The sophism affects anything having a measure of extent.
2) If all elements in the series were F to the same extent, F would be unceasing.
F will not stop in a non arbitrary way.
If rigidity were not gradual, there would be no stiffening. If there are no degrees ± no gradual change.
Smooth change made possible only by degrees.
7c. Degrees of Truth. (RT*) Redundancy Truth: That ‘a is F’ is true is equivalent to a is F.
But the right member is gradual. Therefore, the left member also, by replacement of equivalents.
(GRT) Generalized Redundancy Truth: That ‘a is F’ is ... true is equivalent to a is ... F.
Degrees of truth designated & antidesignated to reflect intermediate stages in the transition.
7d. Minimalism vs. Maximalism. Maximalism holds the Maximalization Rule:
(MR) “p” is true | “p” is completely true.
It is far too demanding. We would be deprived of intermediate cases. Analogy with utilitarianism.
Where the series is open on one side, œx-Fx. But this is 1/4 true. Its negation, ›xFx, is 1/4 false.
If (MR) is unpalatable, and intermediate positions arbitrary, we opt for the Acquiescence Rule:
(AR) “p” is more or less true | “p” is true.
For minimalism, “p” is true provided that it is not completely false.
7e. From Degrees to Contradictions. Something not totally F is partially not F.
A fuzzy case is to some extent F & to some extent not F. Applying (AR) ± contradiction.
7f. Gradual Transition. F diminishes in the same amount as not F augments.
a50 is a soft limit. (SP) and (CP) preserved: their truth ranges from 0.5 to 0.99 true.
Therefore, there is no discontinuity.
Answer to Q1: gradual transition occurs through intermediate stages, by inverse covariance of opposites.
Answer to Q2: F changes because of proportional change in the parameter G.