Notes Predicate Logic
... Quantifiers are applied following a left to right precedence. That is, each quantifier applies to the statement to its right. Thus ∀ x, ∃y, P( x, y) asserts that for each x, it is true that there exists a y, which may depend on x, for which P( x, y) is true. On the other hand ∃ x, ∀y, P( x, y) asser ...
... Quantifiers are applied following a left to right precedence. That is, each quantifier applies to the statement to its right. Thus ∀ x, ∃y, P( x, y) asserts that for each x, it is true that there exists a y, which may depend on x, for which P( x, y) is true. On the other hand ∃ x, ∀y, P( x, y) asser ...
slides (modified) - go here for webmail
... A proof uses a given set of inference rules and axioms. This is called the proof system. Let H be a proof system. ` H φ means: there is a proof of φ in system H whose premises are included in `H is called the provability relation. ...
... A proof uses a given set of inference rules and axioms. This is called the proof system. Let H be a proof system. ` H φ means: there is a proof of φ in system H whose premises are included in `H is called the provability relation. ...
DOC - John Woods
... Metatheory of CPL A big question is, “Why do we bother with proof theory?” After all, its principal concepts – axiom, theorem, deduction, proof – have no intuitive meaning there. What’s the point? Suppose we could show that for each of these uninterpreted properties of CPL’s proof theory theory is a ...
... Metatheory of CPL A big question is, “Why do we bother with proof theory?” After all, its principal concepts – axiom, theorem, deduction, proof – have no intuitive meaning there. What’s the point? Suppose we could show that for each of these uninterpreted properties of CPL’s proof theory theory is a ...
Introduction to Theoretical Computer Science, lesson 3
... …, An are true it holds that the formula B is true as well: A1,…,An |= B: If |=I A1,…, |=I An then |=I B, for all I. Note that the “circumstances“ under which a formula is, or is not, true (see the 1st lesson, Definition 1) are in FOL modelled by interpretations (of predicates and functional symbols ...
... …, An are true it holds that the formula B is true as well: A1,…,An |= B: If |=I A1,…, |=I An then |=I B, for all I. Note that the “circumstances“ under which a formula is, or is not, true (see the 1st lesson, Definition 1) are in FOL modelled by interpretations (of predicates and functional symbols ...
Lecturecise 19 Proofs and Resolution Compactness for
... then interpretation makes it true. Moreover, all other formulas in T are propositional variables set to true, so the interpretation makes T true. Thus, we see that the inductively proved statement holds even in this case. What the infinite formula D breaks is the second part, which, from the existen ...
... then interpretation makes it true. Moreover, all other formulas in T are propositional variables set to true, so the interpretation makes T true. Thus, we see that the inductively proved statement holds even in this case. What the infinite formula D breaks is the second part, which, from the existen ...
