Propositional Logic Predicate Logic

... Definition. A formula A is valid if A is true no matter how we replace the individual constants in A with concrete individuals and the predicate variables in A with concrete predicates. Note. The set of individuals must be instantiated to a non-empty set. This the reason why (∀x.P (x)) ⇒ (∃x.P (x)) ...

... Definition. A formula A is valid if A is true no matter how we replace the individual constants in A with concrete individuals and the predicate variables in A with concrete predicates. Note. The set of individuals must be instantiated to a non-empty set. This the reason why (∀x.P (x)) ⇒ (∃x.P (x)) ...

Handout 14

... where the Ai can be either atomic formulas or their negations. It is thus a conjuction of clauses, i.e. disjunctions of literals (variables or their negations). CNF is used in machine proving of theorems. Resolution in Prolog is also based on a special form of CNF. Definition 5.10 (Disjunctive norma ...

... where the Ai can be either atomic formulas or their negations. It is thus a conjuction of clauses, i.e. disjunctions of literals (variables or their negations). CNF is used in machine proving of theorems. Resolution in Prolog is also based on a special form of CNF. Definition 5.10 (Disjunctive norma ...

Slides

... Let be an unsatisfiable formula Theorem 2: A proof P is complete with respect to if for every full assignment ...

... Let be an unsatisfiable formula Theorem 2: A proof P is complete with respect to if for every full assignment ...

Bound and Free Variables Theorems and Proofs

... using a random process, that puts each edge in with probability 1/2. ...

... using a random process, that puts each edge in with probability 1/2. ...