CPSC 125 Ch 1 sec 1
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This document discusses formal logic and its applications. It defines key concepts in formal logic like statements, logical connectives, truth tables, and tautologies. It explains how formal logic is used in computer science domains like programming languages and circuit design. Formal logic provides a foundation for rigorous and systematic reasoning.
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Heuristic Search Techniques {Artificial Intelligence}
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Similar to CPSC 125 Ch 1 sec 1
Symbolic logic
This document discusses the basics of symbolic logic, including:
1. Statements can be true or false, while questions and commands are not statements. Variables refer to unspecified elements while constants refer to specific elements.
2. Connectives like negation, disjunction, conjunction, implication, and biconditional are used to combine statements and change their truth values.
3. Quantifiers like "all" and "some" are used to make statements about variables. Validity refers to whether a conclusion necessarily follows from given premises. Formal systems of logic aim to prove validity through formal rules of inference.
Math 150 fall 2020 homework 1 due date friday, october 15,
This document contains the homework assignment for Math 150 in Fall 2020. It includes 4 problems to solve and submit by October 15, 2021 at 11:59pm. Problem 1 involves determining if logic formulas are tautologies using reasoning rather than truth tables. Problem 2 gives definitions and asks to prove statements about formulas using induction on complexity. Problem 3 involves proving statements about logical consequence between sets of formulas. Problem 4 asks to determine the truth of statements involving logical consequence between sets of formulas, providing proofs or counterexamples as needed. Practice problems are recommended to work through before attempting the assigned problems.
Meaning and Logic.pptx
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.
2.pdf
The document describes the propositional calculus, which is a formal language used to represent and reason about relationships in the world. It defines the symbols of the propositional calculus, including propositional symbols (P, Q, R), truth values (True, False), and logical connectives (∧, ∨, ¬, →, ≡). Well-formed formulas or sentences in propositional calculus can be built from these symbols using rules. The semantics or truth values of sentences are determined by truth tables, which list all possible truth value assignments. Equivalences between expressions can be shown using truth tables by demonstrating they have identical truth values for all assignments.
3 computing truth tables
This document provides information about symbolic logic, including:
1. It defines propositions as statements that are either true or false, and assigns them the truth values of TRUE or FALSE.
2. It gives examples of propositions and non-examples, and asks the reader to determine if certain statements are propositions.
3. It introduces propositional variables, logical connectives like "and" and "or", and truth tables to evaluate compound propositions formed from variables and connectives.
Proposition Logic in Discrete Structure
This document provides an overview of propositional logic:
1. It defines propositions as statements that can be either true or false, and propositional variables connected by logical connectives like AND and OR.
2. It explains the five main connectives - negation, conjunction, disjunction, implication, and biconditional - and provides their truth tables.
3. It discusses well-formed formulas, tautologies, contradictions, and contingencies. Equivalences between logical statements and duality principles are also covered.
4. Normal forms like CNF and DNF are defined, along with concepts like minterms and maxterms. Rules of inference for building logical arguments are outlined
Logical Connectives (w/ ampersands and arrows)
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.
Logic.pptx
This document provides information about logic and mathematical logic. It begins by asking the reader to answer 10 logic questions. It then defines key logical terms and concepts like propositions, truth tables, logical connectives, and logical operators like negation, conjunction, and disjunction. It provides examples and explanations of how to determine the truth value of simple and compound propositions using truth tables and logical operators. The document aims to explain the foundations and basic components of propositional logic.
Logical connectives
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.
Symbolism And Diagram for Categorical Proposition
This document discusses categorical propositions in classical logic and their symbolic representations. Categorical propositions make claims about whether one class is included in another. They can be symbolized using sets and logical operators. The four basic categorical propositions are A ("All S is P"), E ("No S is P"), I ("Some S is P"), and O ("Some S is not P"). Their relationships can be depicted using Venn diagrams, which visually represent class membership and contradictions between propositions.
Prove asymptotic upper and lower hounds for each of the following sp.pdf
Prove asymptotic upper and lower hounds for each of the following specified otherwise, assume
that in each case, T(n) = 1 (or any small constant) for small value You may assume that n = c^k
for some constant c that you choose. Make your bounds as tight as (No need to specify the
origin of your guess.) T(n0 = 8T(n/3) + n^1.83838383... T(n) = T(n - 1) = 1/n T(n) = 16T(n/2)
+ (n log n)^4. T(n) = 2T(n/2) + n/lg n. T(n) = T(n - 1) + T(n - 2) + 1 with base case of T(1) = 1
and T(2) = 2
Solution
A statement are often outlined as a declaratory sentence, or a part of a sentence, that\'s capable of
getting a truth-value, like being true or false. So, as an example, the subsequent area unit
statements:
George W. Bush is that the forty third President of the us.
Paris is that the capital of France.
Everyone born on Monday has purple hair.
Sometimes, a press release will contain one or a lot of alternative statements as elements.
contemplate as an example, the subsequent statement:
Either Ganymede may be a moon of Jupiter or Ganymede may be a moon of Saturn.
While the on top of sentence is itself a press release, as a result of it\'s true, the 2 elements,
\"Ganymede may be a moon of Jupiter\" and \"Ganymede may be a moon of Saturn\", area unit
themselves statements, as a result of the primary is true and therefore the second is fake.
The term proposition is typically used synonymously with statement. However, it\'s typically
accustomed name one thing abstract that 2 totally different statements with an equivalent which
means area unit each aforementioned to \"express\". during this usage, nation sentence, \"It is
raining\", and therefore the French sentence \"Il pleut\", would be thought-about to specific an
equivalent proposition; equally, the 2 English sentences, \"Callisto orbits Jupiter\" and \"Jupiter
is orbitted by Callisto\" would even be thought-about to specific an equivalent proposition.
However, the character or existence of propositions as abstract meanings continues to be a matter
of philosophical dispute, and for the needs of this text, the phrases \"statement\" and
\"proposition\" area unit used interchangeably.
Propositional logic, conjointly referred to as linguistic string logic, is that branch of logic that
studies ways that of mixing or neutering statements or propositions to create a lot of difficult
statements or propositions. change of integrity 2 easier propositions with the word \"and\" is one
common approach of mixing statements. once 2 statements area unit joined along side \"and\",
the advanced statement fashioned by them is true if and as long as each the element statements
area unit true. owing to this, associate argument of the subsequent kind is logically valid:
Paris is that the capital of France and Paris contains a population of over 2 million.
Therefore, Paris contains a population of over 2 million.
Propositional logic for the most part involves learning logical connectives like the words \"and\"
and \"or\" and therefo.
Maths P.P.T. Connectives
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.
Propositional logic is a good vehicle to introduce basic properties of logic
Propositional logic uses symbols and logical connectives to evaluate the validity of compound statements based on the validity of atomic statements. Natural deduction and resolution are deductive systems that use inference rules to prove statements. Natural deduction is sound and complete, while resolution is also complete. Propositional resolution can check validity by constructing a refutation tree, and linear resolution with Horn clauses is efficient for this task like the logic programming language Prolog.
Similar to CPSC 125 Ch 1 sec 1 (13)
Math 150 fall 2020 homework 1 due date friday, october 15,
Math 150 fall 2020 homework 1 due date friday, october 15,
Prove asymptotic upper and lower hounds for each of the following sp.pdf
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Propositional logic is a good vehicle to introduce basic properties of logic
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CPSC 125 Ch 1 sec 1
- 1. Formal Logic Mathematical Structures for Computer Science Chapter 1 Copyright © 2006 W.H. Freeman & Co., Modified by David Hyland-Wood to correct errors in the original Formal Logic
Editor's Notes
- Remember these! You will need them when doing proofs!
- Relate to Turing’s Halting Problem