The predicate modal logic of provability.

Provability in predicate product logic

We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic, Π∀. By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from Π∀ if and only if it is an L-tautology. As well we characterize the class of lexicographic sums that have this universality property.

The Modal Logic of Pure Provability

We introduce a propositional modal logic PP of “pure” provability in arbitrary theories (propositional or first-order) where the 2 operator means “provable in all extensions”. This modal logic has been considered in another guise by Kripke. An axiomatization and a decision procedure are given and the 23 subtheory is characterized.

Dynamic Modal Predicate Logic

Modal Foundations for Predicate Logic

The complexity of any logical modeling reeects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigatèlighter' versions of this general purpose tool, by modally`deconstructing' the usual semantics, and locating i...

The Semantics of Modal Predicate Logic II. Modal Individuals Revisited

We continue the investigations begun in [10]. We shall define a semantics that is build on a new notion of frame, called coherence frames. In these frames, objects are transcendental (world–independent), as in the standard constant–domain semantics. This will remove the asymmetry between constants and variables of the counterpart semantics of [10]. We demonstrate the completeness of (general) c...