Sentence examples for propositional consequence from inspiring English sources

(For a general discussion, see the entry on propositional consequence relations and algebraic logic).

For example we define classical propositional consequence by means of truth valuations, first-order consequence relation by means of structures, the intuitionistic consequence relation by means of Kripke models, etc.

In this entry we concentrate on the general theory of the algebraization of propositional logics taken as consequence relations.

Note that the conclusions of all RDR trees within an NRDR knowledge base are propositional values, therefore any consequence (beta ) has a propositional value (see Definition 1 in Sect. 4.1.1 for semantics of rules in an RDR tree).

The main theorems in turn yielded Boole's General Method for analyzing the consequences of propositional premises.

On this view, propositions and propositional functions have an order.

Valid inferences among propositions are reflected by the provable formulas, because (for any A and B) A ⊃ B is provable if and only if B is always a logical consequence of A. The propositional calculus is consistent in that there exists no formula in it such that both A and ∼A are provable.

contends that EC has implausible consequences for reports of propositional attitudes.

The research on logic systems described in the previous sections has been extended to encompass other consequence relations that go beyond propositional logics, like equational logics and the consequence relations between sequents built from the formulas of a propositional language definable using sequent calculi.

As a consequence, most solvers for the propositional satisfiability problem (SAT) expose parameters that allow them to be customized to a particular family of instances.

Consequences for all defaults are propositional values.