Propositional and Predicate Calculus - Carleton University
Propositional and Predicate Calculus - Carleton University
Propositional and Predicate Calculus - Carleton University
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Outline <strong>and</strong> Introduction<br />
<strong>Propositional</strong> <strong>Calculus</strong><br />
<strong>Predicate</strong> <strong>Calculus</strong><br />
Inference Rules<br />
Unification<br />
Resolution Theorem Proving<br />
<strong>Predicate</strong>s <strong>Calculus</strong> Sentences<br />
DEFINITION<br />
PREDICATE CALCULUS SENTENCES<br />
Every atomic sentence is a sentence.<br />
1. If s is a sentence, so is its negation, ¬s<br />
Introduction<br />
<strong>Predicate</strong>s <strong>and</strong> Sentences: Syntax<br />
General Important Notes<br />
Atomic Sentences<br />
<strong>Predicate</strong> <strong>Calculus</strong>: Semantics<br />
<strong>Predicate</strong> Equivalences<br />
Some Examples<br />
2. If s 1 <strong>and</strong> s 2 are sentences, then so is their conjunction s 1 ∧ s 2<br />
3. If s 1 <strong>and</strong> s 2 are sentences, then so is their disjunction s 1 ∨ s 2<br />
4. If s 1 <strong>and</strong> s 2 are sentences, then so is their implication s 1 → s 2<br />
5. If s 1 <strong>and</strong> s 2 are sentences, then so is their equivalence s 1 ≡ s 2<br />
6. If X is a variable <strong>and</strong> s a sentence, then ∀X s is a sentence.<br />
7. If X is a varaible <strong>and</strong> s a sentence, then ∃X s is a sentence.
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