Predicate logic proof

• Can a logical proof be used on a subformula?

  Predicate Logic Proofs • Can use – Predicate logic inference rules whole formulas only – Predicate logic equivalences (De Morgan’s) even on subformulas – Propositional logic inference rules whole formulas only – Propositional logic equivalences even on subformulas Predicate Logic Proofs with more content

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• What is the difference between propositional logic equivalences and predicate logic inferences?

  Predicate logic inference rules whole formulas only – Predicate logic equivalences (De Morgan’s) even on subformulas – Propositional logic inference rules whole formulas only – Propositional logic equivalences even on subformulas Last Class: Predicate Logic Proof Prove ∀x P(x)→∃x P(x)

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• What is a predicate logic?

  To translate expressions like every man and some man, Predicate Logic includes variables and quantifiers to bind the variables. What remains is to give a formal definition of Predicate Logic, its syntax and its semantics, and to reformulate what we mean by a model to fit this new logic.

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• What is the smallest sentence in predicate logic?

  The smallest English sentence is formed by combining a verb with a subject. In Predicate Logic, the smallest proposition is formed by combining a predicate with an individual. Predicates correspond to verbs and individuals correspond to subjects and objects. The parallel is presented in (5). 2. The Basic Elements of Predicate Logic

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• [PDF File]CSE 311 Lecture 08: Inference Rules and Proofs for Predicate ...

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  Proving implications with the direct proof rule Direct Proof Rule The premise means “Given , we can prove .” So the direct proof rule says that if we have such a proof, then we can conclude that is true. Example: prove . 1.1. Assumption 1.2. Elim : 1.1 1.3. Intro : 1.2 2. Direct Proof Rule A B ∴ A → B A B A B A → B (p∧q) → (p∨q ...

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• [PDF File]Lecture 8: Predicate Logic Proofs - University of Washington

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  Predicate Logic Proofs with more content • In propositional logic we could just write down other propositional logic statements as “givens” • Here, we also want to be able to use domain knowledge so proofs are about something specific • Example: • Given the basic properties of arithmetic on integers, define: Even(x) ≡ ∃y (x = 2⋅y)

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• [PDF File]Predicate Logic - Scholars at Harvard

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  Predicate Logic Yimei Xiang yxiang@fas.harvard.edu 18 February 2014 1 Review 1.1 Set theory 1.2 Propositional Logic Connectives Syntax of propositional logic: { A recursive de nition of well-formed formulas { Abbreviation rules Semantics of propositional logic: { Truth tables { Logical equivalence { Tautologies, contradictions, contingencies ...

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• [PDF File]Lecture 8: Predicate Logic Proofs, English Proofs

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  – almost all math (and theory CS) done in Predicate Logic • But they are tedious and impractical – e.g., applications of commutativity and associativity – Russell & Whitehead’s formal proof that 1+1 = 2 appears after more than 100 pages of build up – we allowed ourselves to cite “Arithmetic”, “Algebra”, etc.

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• [PDF File]Lecture 7: Propositional & Predicate Logic Proofs

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  My First Predicate Logic Proof Prove ∀x P(x) → ∃x P(x) 1. Direct Proof 1.1. Assumption 1.2. Elim∀: 1.1 1.3. Intro ∃: 1.2 Working forwards as well as backwards: In applying “Intro ∃” rule we didn’t know what expression we might be able to prove P(c) for, so we worked forwards to figure out what might work.

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• [PDF File]The Syntax of Predicate Logic - Boston University

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  (5) a. Object Language b. Predicate Logic Sentence (S) Wff qp qp Subject (NP) Verb (VP) Predicate Argument 2. The Basic Elements of Predicate Logic To strengthen your understanding of Predicate Logic and its basic elements, let me first appeal to your intuitions. Consider the sentences in (6). (6) a. Aristotle is a man b. Socrates is a man

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