PPT-Propositional Equivalences

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. 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 stoichiometric equivalences stoichiometric mole ratios Mole-to-Mole Conversions Need to write what you know as propositional formulas. Theorem proving will then tell you whether a given new sentence will hold given what you know. Three kinds of queries. Is my . knowledgebase . consistent? (i.e. is there at least one world where everything I know is true?) . Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. 1. Propositions. A . proposition. is a declarative sentence that is either true or false.. Examples of propositions:. The Moon is made of green cheese.. Trenton is the capital of New Jersey.. Toronto is the capital of Canada.. The Syntax and Semantics of PL. Languages in General. All languages have a set of symbols, rules for constructing compound constructions out of atomic constructions, and meanings assigned to the significant units.. Section 1.1. Propositions. A . proposition. is a declarative sentence that is either true or false.. Examples of propositions:. The Moon is made of green cheese.. Trenton is the capital of New Jersey.. Goal: . Show . how . propositional equivalences . are established . & introduce . the most . important such . equivalences.. Copyright © Peter . Cappello. 2. Equivalence. Name. p .  T . ≡ p; p . 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 . 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 . Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . 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. 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..