# predicate logic examples proofs

Such an alogithm could be used to decide satisﬁable of ﬁrst-order pred-icate logic sentences. Still have two truth values for statements (T and F) ! Mary loves … Two parts: ! x∈A x∈B ----- ∃y∈Ay∈B ?? I. A predicate P describes a relation or property. • A predicate is a property that is affirmed or denied about the subject (in logic, we say ‘variable’ or ‘argument’) of a statement • Consider the statement : ‘x is greater than 3’ – ‘x’ is the subject – ‘is greater than 3’ is the predicate Proofs in predicate logic can be carried out in a manner similar to proofs in propositional logic (Sections 14.8 and 14.9). Illinois Institute of Technology Class 2 … When we assign values to x and y, then P has a truth value. b) Translate your set-theoretic notation into the notation of predicate logic. predicate logic. •Use the definition of entailment directly. Inference Rules 3. Statements in Predicate Logic P(x,y) ! Variables (x,y) can take arbitrary values from some domain. In this course we are concerned with the transcription using given predicate symbols and the universe. Since they are more highly patterned than most proofs, they are a good place to start. •In practice, can be much faster… •Polynomial-time inference procedure exists when KB is expressed as Horn clauses: where the P i and Q are non-negated atoms. For this reason, I'll start by discussing logic proofs. Example: Using (p → q) 㱻 (¬p ∨ q) for r, p for p, and ¬¬p for q, by substitution, we know (¬¬p → q) 㱻 (¬p ∨ q). ! Consequence There is no algorithm that decides whether a ﬁrst-order predi-cate logic sentence is a tautology. More Answers for Practice in Logic and HW 1.doc Ling 310 Feb 27, 2006 1 More Answers for Practice in Logic and HW 1 This is an expanded version showing additional right and wrong answers. You can't expect to do proofs by following rules, memorizing formulas, or looking at a few examples in a book. The use of symbolic logic also makes reasoning formal and mechanical, contributing to the simplification of the reasoning and making it less prone to errors. The patterns which proofs follow are complicated, and there are a lot of them. Some tautologies of predicate logic are analogs of tautologies for propo-sitional logic (Section 14.6), while others are not (Section 14.7). Predicate Logic 4. c) Give a proof that the syllogism is valid, similar to that given in the lecture 5 videos. 1. Transcribing English sentences into wffs is sometimes a non-trivial task. –First-Order logic •Godel’s completeness theorem showed that a proof Proof. Practice in 1st-order predicate logic – with answers. 1. The rules of inference are the essential building block in the construction of valid arguments. Inference rules for propositional logic plus additional ... some of the example proofs to follow. We will learn Proof procedure is exponential in n, the number of symbols. E. Sample Proofs • Proofs in predicate logic give step-by-step reasoning for why we think the truth of one proposition is related to another. ! A ﬁrst-order predicate logic sentence G is satisﬁable if, and only if, :G is not a tautology. In Section 14.10 we discuss some of the implications of predicate logic as to our Propositional Logic 2. • end of proof CS 441 Discrete mathematics for CS M. Hauskrecht Informal proofs Proving theorems in practice: • The steps of the proofs are not expressed in any formal language as e.g.