Knowledge bases are currently being investigated by database researchers in order to extend the expressiveness of the relational model to include deductive capabilities in the form of rules. The motivation behind this paper is to present a formalism which extends the relational approach to homogeneous distributed databases to the knowledge base paradigm. The basis of our formalism of distribute...

The fusion Ll Lr of two normal modal logics formulated in languages with disjoint sets of modal operators is the smallest normal modal logic containing Ll [ Lr. This paper proves that decidability, interpolation, uniform interpolation, and Halld encompleteness are preserved under forming fusions of normal polyadic polymodal logics. Those problems remained open in [Fine & Schurz [3]] and [Kracht...

Justification logics refine modal logics by replacing the usual necessity operator with a family of justification terms that embody reasons for the necessity of a formula, rather than simply recording the fact of necessity. Many common modal logics have justification counterparts. The connection between a modal logic and its justification counterpart is through a Realization Theorem, which says...

Van Fraassen’s modal interpretation of non-relativist quantum mechanics (QM) is articulated to support an antirealist account of QM. However, given the particular form of van Fraassen’s anti-realism (constructive empiricism), two problems arise when we try to make it compatible with the modal interpretation: one difficulty concerns the tension between the need for modal operators in the modal i...

We analyse the role of the modal axiom corresponding to the first-order formula “∃y (x = y)” in axiomatisations of two-dimensional propositional modal logics. One of the several possible connections between propositional multi-modal logics and classical first-order logic is to consider finite variable fragments of the latter as ‘multi-dimensional’ modal formalisms: First-order variable-assignme...

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...

Van Fraassen’s modal interpretation of nonrelativistic quantum mechanics is articulated to support an anti-realist account of quantum theory. However, given the particular form of van Fraassen’s anti-realism (constructive empiricism), two problems arise when we try to make it compatible with the modal interpretation: one difficulty concerns the tension between the need for modal operators in th...

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...

In this paper we show how defeasible logic could formally account for the non-monotonic properties involved in motivational attitudes like intention and obligation. Usually, normal modal operators are used to represent such attitudes wherein classical logical consequence and the rule of necessitation comes into play, i.e., ` A/ ` 2A, that is from ` A derive ` 2A. This means that such formalisms...

We study prefixed tableaux for first-order multi-modal logic, providing proofs for soundness and completeness theorems, a Herbrand theorem on deductions describing the use of Herbrand or Skolem terms in place of parameters in proofs, and a lifting theorem describing the use of variables and constraints to describe instantiation. The general development applies uniformly across a range of regime...