We investigate the modal logic of the generic multiverse which is a bimodal logic with operators corresponding to the relations “is a forcing extension of” and “is a ground model of”. The fragment of the first relation is the modal logic of forcing and was studied by the authors in earlier work. The fragment of the second relation is the modal logic of grounds and will be studied here for the f...

This paper presents an overview of the development of the eld of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the sim...

Higher dimensional automata (HDA) are a model of concurrency that can express most of the traditional partial order models like Mazurkiewicz traces, pomsets, event structures, or Petri nets. Modal logics, interpreted over Kripke structures, are the logics for reasoning about sequential behavior and interleaved concurrency. Modal logic is a well behaved subset of first-order logic; many variants...

We present and study a Modal Access Control Logic (MACL) to specify and reason about access control policies. We identify canonical properties of well-known access control axioms. We provide a Hilbert-style proof-system and we prove soundness, completeness and decidability of the logic. We present a sound and complete embedding of Modal Access Control Logic into First-Order Logic. We show how t...

In this paper we continue our research in computational complexity of fragments of a particular belief-desire-intention (BDI) logic for cooperative problem solving (CPS) called TeamLog. The logic in question combines propositional multi-modal logic to express static aspects of CPS with propositional dynamic logic used for dynamic aspects of CPS. We concentrate here on the static fragment of the...

1 In this paper we consider approaches to belief revision and contraction in modal logics that are based on a translation of an agent’s beliefs in modal logic to first-order logic, where revision or contraction is performed before translating the result back into the original modal language. Contraction presents a unique problem, as theorems of the modal language can be accidentally removed, wh...

Deciding whether a modal formula is satisfiable with respect to a given set of (global) assumptions is a question of fundamental importance in applications of logic in computer science. Tableau methods have proved extremely versatile for solving this problem for many different individual logics but they typically do not meet the known complexity bounds for the logics in question. Recently, it h...

I introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic. In order for the paper to be self-contained, I also recall the etymology and definition of neutrosophy and of neutrosophic logic. Several example...

Bisimulation quantifiers are a natural extension of modal logics. They preserve the bisimulation invariance of modal logic, while allowing monadic second-order expressivity. Unfortunately, it is not the case that extension by bisimulation quantifiers always preserves the decidability of a modal logic. Here we examine a general class of modal logics for which decidability is preserved under exte...

This paper presents a general method for proving termination of tableaux-based procedures for modal-type logics and related firstorder fragments. The method is based on connections between filtration arguments and a general blocking technique. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be ap...