... We say that cp is valid in M, and write M i= cp, if (M, w ) i= cp for all respect to 9). w E W,. We then define (T FA cp to hold if M .[a] implies M t= ~ [ c p ] for all M E A and all substitutions 7. For example, defining truth in modal logic with respect to pairs ( M ,w) consisting of a Kripke str ...
notes
... Relative completeness follows by a simple argument: Proof Sketch. Let c be a command and let P and Q be assertions such that the partial correctness specification {P } c {Q} is valid. By Lemma 1 we have ⊨ P =⇒ wlp(c, Q). By Lemma 2 we have ⊢ {wlp(c, Q)} c {Q}. We conclude ⊢ {P } c {Q} using the C ON ...
... Relative completeness follows by a simple argument: Proof Sketch. Let c be a command and let P and Q be assertions such that the partial correctness specification {P } c {Q} is valid. By Lemma 1 we have ⊨ P =⇒ wlp(c, Q). By Lemma 2 we have ⊢ {wlp(c, Q)} c {Q}. We conclude ⊢ {P } c {Q} using the C ON ...
notes
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
Supervaluationism and Classical Logic
... classically follows that it is not the case that for any time x if Julia is a baby at x then Julia is a baby at time x + 1, classically in other words, there is a time x such that Julia is a baby at x but Julia is not a baby at x + 1 second. Epistemicists in vagueness want to retain classical logic ...
... classically follows that it is not the case that for any time x if Julia is a baby at x then Julia is a baby at time x + 1, classically in other words, there is a time x such that Julia is a baby at x but Julia is not a baby at x + 1 second. Epistemicists in vagueness want to retain classical logic ...
p - Upm
... establishing the validity of an argument the method of Proof by Contradiction. The idea behind the method of Proof by Contradiction is to establish a statement (namely, the conclusion of an argument) by showing that, if this statement were false, then we would be able to deduce a contradiction (p ...
... establishing the validity of an argument the method of Proof by Contradiction. The idea behind the method of Proof by Contradiction is to establish a statement (namely, the conclusion of an argument) by showing that, if this statement were false, then we would be able to deduce a contradiction (p ...
Introduction to Proofs, Rules of Equivalence, Rules of
... follows from, but is not identical to, the truth of the source lines. • Operate on lines whose statement forms match the statement forms of the lines in the argument form of the rule. • Can be applied ONLY to entire lines, not parts of lines. ...
... follows from, but is not identical to, the truth of the source lines. • Operate on lines whose statement forms match the statement forms of the lines in the argument form of the rule. • Can be applied ONLY to entire lines, not parts of lines. ...
Logic and Reasoning
... fallacy is present in the following statements: – “The Ford Explorer is the most popular SUV on the market, so it must be the safest.” – “You were the only person working when the accident happened so it must be your fault.” – “If you don’t finish this paper, you will become a bum and live in a van ...
... fallacy is present in the following statements: – “The Ford Explorer is the most popular SUV on the market, so it must be the safest.” – “You were the only person working when the accident happened so it must be your fault.” – “If you don’t finish this paper, you will become a bum and live in a van ...