Sentence examples for sentence p from inspiring English sources

If the system is complete, then either the sentence p or its negation is a theorem of the system.

Representing expressions by numbers and using an ingenious substitution function, Gödel was able to find in the system a sentence p that could be viewed as expressing (2).

Moreover, the undecidable sentence p is always of a relatively simple form namely, the form (∀x A x), "For every x, x is A," in which A is a recursive, in fact a primitive recursive, predicate.

A concept more general than validity is that of the relation of logical entailment or implication between a possibly infinite set X of sentences and a single sentence p that holds if and only if p is true in every model of X.

{i|Ri [ f(i), g(i)]} ∊ D. The central theorems are the following: If i (i ∊ I) are realizations of the same language, then a sentence p is true in the ultraproduct U if and only if the set of i such that p is true in i belongs to D. In particular, if each i is a model of a theory, then U is also a model of the theory.

Hence, suppose that the belief set contains the sentence p, "Shakespeare wrote Hamlet".

The special case when for all sentences p, γ(K⊥p) has exactly one element is called maxichoice contraction.

A selection function for a belief set K should, for all sentences p, select those elements of K⊥p that are "best", or most worth retaining.

Noam Chomsky showed that children can learn to speak thanks to an "innate grammar," a template for arranging words in meaningful sentences (p. 191).

Consider a language with three atomic sentences, p, q, and r, and an information state consisting of three worlds, wpq, wqr, and wpr, where the subscripts of each world indicate which atomic sentences are true at that world.

Further, if propositions are sets of possible worlds, belief is construed as a relation between individuals and propositions and sentences of the form 'A believes that P' assert that the individual A stands in the belief relation to the proposition expressed by 'P', then for any necessarily equivalent sentences 'P' and 'Q', 'A believes that P' and 'A believes that Q' cannot differ in truth value.