A resolution framework for finitely-valued first-order logics

First-Order Resolution Methods for Modal Logics

In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution. Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDL-like dynamic modal logics whic...

On finitely-valued Fuzzy Description Logics

Minimal Sequent Calculi for Lukasiewicz’s Finitely-valued Logics

The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Lukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place sequent calculus (in the sense of [10, 9]) with the cut-elimination property and a strong completeness with respect to the logic involved which is most compact among similar ...

Elimination of Cuts in First-order Finite-valued Logics

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledgerepresentation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about...

Many-Valued First-Order Logics with Probabilistic Semantics

We present n-valued rst-order logics with a purely proba-bilistic semantics. We then introduce a new probabilistic semantics of n-valued rst-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics Ln. Within this semantics, closed formulas of classical rst-order logics that are logically equivalent in the classical ...