PPT-1 Propositional Equivalences

From Aaron Bloomfield Used by Dr Kotamarti 2 Tautology and Contradiction A tautology is a statement that is always true p p will always be true Negation Law A contradiction is a statement that is always false. Backbones of propositional theories are literals that are true in every model Backbones have been used for characteri zing the hardness of decision and optimization problems Moreov er back bones 64257nd other applications For example backbones are o 1. Tautologies, Contradictions, and Contingencies. A . tautology. is a proposition that is always . true. .. Example: . p. . ∨¬. p. . A . contradiction. is a proposition that is always . false. mindread. ?. Tadeusz. Zawidzki, GWU, Philosophy, MBEC, . zawidzki@gwu.edu. KNEW 2013, . Kazimierz. . Dolny. , Poland. Overview. What I mean by “mindreading”. What I mean by “why”. The received view and its discontents. Use . WalkSAT. Use min-Conflict heuristic. Similar to hill climbing and simulated annealing. Pick unsatisfied clause then pick a symbol to flip to satisfy the clause by. Use Min Conflict. Or Random. Downside. DEFINITION 1. A compound proposition that is always true, no matter what the truth values of the propositions that occur in it, is called . a tautology. .. A compound proposition that is always false is called. Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. 1. In . logic. , a . tautology. (from the . Greek. word τα. υτολογί. α) is a . formula. that is true in every possible . interpretation. .. Philosopher. . Ludwig Wittgenstein. first applied the term to redundancies of . . Iddo Tzameret. Royal Holloway, University of London . Joint work with Fu Li (Tsinghua) and Zhengyu Wang (Harvard). . Sketch. 2. Sketch. : a major open problem in . proof complexity . stems from seemingly weak results. Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . Introduction and Scope:. Propositions. Fall. 2017. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . supporting . Section 1.3. Section Summary. Tautologies, Contradictions, and Contingencies. . Logical Equivalence. Important Logical Equivalences. Showing Logical Equivalence. Normal Forms (. optional, covered in exercises in text. Lecture Notes. April 17th. Two Topics. Homework 9. Grammar and Logic. Homework 9. Use . cosines.py. . or . bfs4.perl . (or some . nltk. similarity measure mentioned in a previous lecture) or a mix of the two to come up with a method of matching words to (simple) definitions for quizzes A and B (shown on the next slides). September 24. th. 2013.. Religious Experience: Revelation Through Sacred Texts. Revelation. Revelation. : Knowledge that is gained through the agency of God. Direct from an infallible source and unconditioned..