First-order modal logics have many applications, e.g. in planning and program verification. Whereas comprehensive and standardized problem libraries exist for, e.g., classical (TPTP library) and intuitionistic (ILTP library) logic, nothing comparable is so far available for firstorder modal logics. The aim of the Quantified Modal Logic Theorem Proving (QMLTP) library is to close this gap by pro...

Understanding modal predicate logic is a continuing challenge, both philosophical and mathematical. In this paper, I study this system in terms of frame correspondences, finding a number of definability results using substitution methods, including new analyses of axioms in intermediate intuitionistic predicate logics. The semantic arguments often have a different flavour from those in proposit...

In this paper, we present a logical framework for integrating the quantitative and qualitative approaches to uncertainty management based on possibility theory. The semantics of the logic is based on the Dempster’s rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilist...

We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation’s characterization of a hierarchy of pseudovarieties of finite lattices, progressively generalizing finite distributive lattices. This formal connection is mediated through monotone modal logic. Indeed, we adapt the correspondence algorithm ...

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possi...

We present two modal typing systems with the approximation modality, which has been proposed by the author to capture selfreferences involved in computer programs and their speci cations. The systems are based on the simple and the F-semantics of types, respectively, and correspond to the same modal logic, which is considered the intuitionistic version of the logic of provability. We also show ...

We consider second order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem-Rosen theorem and the GoldblattThomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of S...

A dialogical version of (modal) epistemic logic is outlined, with an intuitionistic variant. Another version of dialogical epistemic logic is then provided by means of the S4 mapping of intuitionistic logic. Both systems cast new light on the relationship between intuitionism, modal logic and dialogical games.

A dialogical version of (modal) epistemic logic is outlined, with an intuitionistic variant. Another version of dialogical epistemic logic is then provided by means of the S4 mapping of intuitionistic logic. Both systems cast new light on the relationship between intuitionism, modal logic and dialogical games.

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its ne...