* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Homework 5
Survey
Document related concepts
Abductive reasoning wikipedia , lookup
Structure (mathematical logic) wikipedia , lookup
Modal logic wikipedia , lookup
Model theory wikipedia , lookup
Quantum logic wikipedia , lookup
History of logic wikipedia , lookup
Combinatory logic wikipedia , lookup
Boolean satisfiability problem wikipedia , lookup
Natural deduction wikipedia , lookup
Mathematical logic wikipedia , lookup
Propositional formula wikipedia , lookup
Interpretation (logic) wikipedia , lookup
Mathematical proof wikipedia , lookup
Law of thought wikipedia , lookup
First-order logic wikipedia , lookup
Laws of Form wikipedia , lookup
Curry–Howard correspondence wikipedia , lookup
Transcript
Applied Logic CS 4860 Spring 2009 Homework 5 Due Date: Tuesday, March 31, 2009 Reading Please read pp. 57–65 in Smullyan for Tuesday, March 24. Project Work During the second half of this course you should work on a self-chosen project related to the topic of applied logic. This could, for instance, be a literature study about an interesting or the implementation (and documentation) of a proof environment. We will discuss a few possibilities in class. Please prepare a project proposal (about half a page) for Tuesday, March 31. Questions (1) Reduce these P 2 formulas to purely propositional formulas. (a) (∀p) p ⊃ ⊥ (b) (∀p)(∀q) ((∼p ∨ q)⊃(p⊃q)) (c) (∀p)(∀q) ((p⊃p ∨ q) ∧ (p ∧ q⊃p)) (2) Give Refinement logic rules for P 2 . (3) Construct an example of a formula that is satisfiable in a denumerable universe but not in any finite one (exercise 3, page 50 of Smullyan). (4) Show that a first-order formula A is valid if and only if ∼A is satisfiable. Show that A is satisfiable if and only if ∼A is valid (exercise 4, page 50 of Smullyan). (5) Bonus (1): There is a simple proof for cut elimination in P 2 . State the theorem and outline a proof. Details are not necessary. (6) Bonus (2): Solve exercise 3, page 52 of Smullyan. 1