In this paper we develop a 2-valued reduction of many-valued logics, into 2-valued multi-modal logics. Such an approach is based on the contextualization of many-valued logics with the introduction of higher-order Herbrand interpretation types, where we explicitly introduce the coexistence of a set of algebraic truth values of original many-valued logic, transformed as parameters (or possible w...

There are two well investigated approaches to automate reasoning in modal logics: the direct approach and the translational approach. The direct approach [6, 7, 14, 27] develops specific calculi and tools for the task; the translational approach [29, 30] transforms modal logic formulas into firstorder logic and applies standard first-order tools. Embeddings of modal logics into higher-order log...

Modal logic was originally conceived as the logic of necessary and possible truths. It is now viewed more broadly as the study of many linguistic constructions that qualify the truth conditions of statements, including statements concerning knowledge, belief, temporal discourse, and ethics. Most recently, modal symbolism and model theory have been put to use in computer science, to formalise re...

Sahlqvist-style correspondence results remain a perennial theme and an active topic of research within modal logic. Recently, there has been interest in extending the classical results in this area to the modal mu-calculus [7]. For instance, in [8] van Benthem, Bezhanishvili and Hodkinson define a class of Sahlqvist formulas for the modal mu-calculus, all of which have frame correspondents in f...

Unified Correspondence. Correspondence and completeness theory have a long history in modal logic, and they are referred to as the “three pillars of wisdom supporting the edifice of modal logic” [22, page 331] together with duality theory. Dating back to [20,21], the Sahlqvist theorem gives a syntactic definition of a class of modal formulas, the Sahlqvist class, each member of which defines an...

It is widely agreed that the modular method is one of the most effective methods to specify and verify complex systems in order to avoid combinatorial explosion. FLC ( Fixpoint Logic with Chop) is an important modal logic because of its expressivity and logic properties, e.g., it is strictly more expressive than the μ-calculus. In this paper, we study the compositionality of FLC, namely, to inv...

In this paper we introduce a logic of abstract argumentation capturing Dung’s theory of abstract argumentation, based on connectives for attack and defend. We extend it to a modal logic of abstract argumentation to generalize Dung’s theory and define variants of it. Moreover, we use the logic to relate Dung’s theory of abstract argumentation to more traditional conditional and comparative forma...

In this paper we introduce a logic of abstract argumentation capturing Dung’s theory of abstract argumentation, based on connectives for attack and defend. We extend it to a modal logic of abstract argumentation to generalize Dung’s theory and define variants of it. Moreover, we use the logic to relate Dung’s theory of abstract argumentation to more traditional conditional and comparative forma...

Hybrid logics extends modal logic with a special sort of variables, called nominals, which are evaluated to singletons in Kripke models by valuations, thus acting as names for states in models, see e.g., [1], [2] and [7]. Various other connectives which capitalize on this naming power of the nominals and, in so doing, enhance the expressive power of these languages even further, can be included...