Logic is generally defined as the science of reasoning. Mathematical logic is mainly concerned with forms of reasoning that lead from true premises to true conclusions. Thus we say that the argument from σ0;σ1; · · · ;σn−1 to δ is logically correct if whenever σi is true for all i < n, then so is δ. In place of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is v...

We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal veri cation of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints | a central notion in hardware veri cation | as a logical modality. The resulting logic is unorthodox in several respects. As a modal logic it is...

Adam Brandenburger and H. Jerome Keisler have recently discovered a two person Russell-style paradox. They show that the following configurations of beliefs is impossible: Ann believes that Bob assumes that Ann believes that Bob’s assumption is wrong. In [7] a modal logic interpretation of this paradox is proposed. The idea is to introduce two modal operators intended to represent the agents’ b...

Recent work within the eld of Categorial Grammar has seen the development of approaches that allow diierent modes of logical behaviour to be displayed within a single system, something corresponding to making available diiering modes of linguistic description. Earlier attempts to achieve this goal have employed modal operators called structural modalities, whose use presents a number of problem...

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T , uses a single modal operator ∇T of arity given by the functor T itself, and its semantics is defined in term...

In a recent paper, we presented a new logic called ES for reasoning about the knowledge, action, and perception of an agent. Although formulated using modal operators, we argued that the language was in fact a dialect of the situation calculus but with the situation terms suppressed. This allowed us to develop a clean and workable semantics for the language without piggybacking on the generic T...

Graded modal logic GS5 is an extension of S5 by the modal connective } : the formula } A means that there are at least worlds satisfying A. In this paper, we show how to reduce GS5 satisfiability to propositional satisfiability (SAT). Furthermore, we consider a satisfiability problem related to the frequent itemset mining problem: SUPPSAT (where n is a strictly positive integer). We show how SU...

We study a branching-time temporal logic of belief revision where the interaction of belief and information is modeled explicitly. The logic is based on three modal operators: a belief operator, an information operator and a next-time operator. We consider three logics of increasing strength. The …rst captures the most basic notion of minimal belief revision. The second characterizes the qualit...

It is well known that the standard 3-valued logic programs with constraints can be inconsistent. Because of that we can not use it for a data integration where mutually inconsistent information comes from different data sources. We argue that a natural way to answer to this challenge, without collapsing all sentences into inconsistency, is by passing to 4-valued bilattice-based logic (with logi...

RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities. We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents’ subjective interpretations of these systems. Categorization systems are a...