Truth, deduction, computation lecture 7
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This document discusses natural deduction and the rules of Boolean logic and formal proofs. It introduces natural deduction as a proof calculus that uses inference rules to model human reasoning. The document then explains introduction and elimination rules for conjunction, disjunction, negation and the contradiction symbol ⊥. It notes that the rules allow deducing ⊥ from a tautological, logical or meaning-based contradiction. The document emphasizes being careful with the rules, finding counterexamples if deductions don't make sense, and formalizing proofs by tracking arguments back to their sources. It also notes that at times deductions can be made without premises.
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
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- 1. Truth, Deduction, Computation Lecture 7 Boolean Logic and Formal Proofs Vlad Patryshev SCU 2013
- 2. Natural Deduction A proof calculus that: ● has inference rules ● models actual human reasoning
- 3. Natural Deduction ● introduction rules ● elimination rules ● shortcuts (“rule defaults”)
- 4. Conjunction Rules Elimination (∧ Elim) P1∧P2∧...Pi∧... ∧Pn Pi Do we need n here?!
- 5. Conjunction Rules Introduction (∧ Intro) P1 . . . Pn P1∧P2∧...Pi∧... ∧Pn Do we need n here?!
- 6. Disjunction Rules Introduction (v Intro) Pi P1vP2v...Piv...vPn Do we need n here?!
- 7. Disjunction Rules Elimination (v Elim) Example P1vP2v...vPn P1 } S subproof . . . Pn S S Do we need n here?!
- 8. Negation Rules Elimination (¬ Elim) ¬¬P … P
- 9. Negation Rules Introduction (¬ Intro) P ⊥ ¬P
- 10. ⊥ Rules Introduction (⊥ Intro) P ¬P ⊥
- 11. ⊥ Rules Elimination (⊥ Elim) ⊥ P
- 12. All These Negation Rules
- 13. More ⊥ Rules in Fitch ● Taut Con: If you can deduce a TT-contradiction, you can deduce ⊥ ● FO Con: If you can deduce a logical contradiction, you can deduce ⊥ ● Ana Con: If you can deduce sentences that are contradictory due to the meaning of predicates, you can deduce ⊥
- 14. Rules - be careful Bad Example
- 15. Now that you know the rules... ● ● ● ● Remember the meaning of sentences Trust the past Find a counterexample if you don’t To formalize your proof, track back your arguments - “where did this come from?” ● … use Fitch…
- 16. At times you don’t need premises! E.g.
- 17. That’s it for today