Sentence examples for modal logic a from inspiring English sources

More generally, we will call a modal logic a Geach logic if it can be axiomatized by adding a finite set of Geach schemes to \({\textsf{K}}\).

RE is the fundamental rule for "Classical Systems of Modal Logic", a class that includes normal modal logics as a proper subset.

The first-order language under consideration has a 1-place predicate symbol p* corresponding to each ordinary propositional symbol p of modal logic, a 2-place predicate symbol R, and a 2-place predicate symbol =.

This is obtained by adding to ordinary modal logic a second sort of propositional symbols called nominals such that in the Kripke semantics each nominal is true relative to exactly one point.

When Prior arrived at UCLA Nino Cocchiarella was just completing a Ph.D. thesis on quantified modal and tense logic under Montague's supervision ('Tense and Modal Logic: A Study in the Topology of Temporal Reference').

For example, in Modal Logic a Replacement Theorem holds just as it does classically: if \(X \equiv X'\) is provable in a normal modal logic then so is \(F \equiv F '\) where \(F\) is a formula and \(F'\) is like \(F\) except that some subformula occurrence \(X\) has been replaced with \(X'\).

The phenomenon of having a modal logic with a justification logic counterpart has turned out to be unexpectedly broad, and the implications of this are not yet understood.

Even though propositional provability logic is a modal logic with a kind of "necessity" operator, it withstands Quine's (1976) controversial critique of modal notions as unintelligible, already because of its clear and unambiguous arithmetic interpretation.

Some examples of the many interesting topics dealt with include results on decidability (whether it is possible to compute whether a formula of a given modal logic is a theorem) and complexity (the costs in time and memory needed to compute such facts about modal logics).

A matrix for a modal logic M extends a matrix for a propositional logic by adding a unary function that corresponds to the connective ◊.

Kripke's 1959 "A Completeness Theorem in Modal Logic" contains a model theoretic completeness result for a quantified version of S5 with identity.