Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Logic Closure Spaces, SLCS, extends with reachability connectives that, in turn, can be used expressing interesting spatial properties, such as "being near to" or surrounded by". SLCS constitutes kernel solid logical framework reasoning abo...

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add, and swap edges in the model, both locally and globally. We provide translations from these logics to hybrid logic along with an implementation....

By a predicate we mean a term in the HOL logic of type *-> bool, where * can be any type. Boolean connectives, quantiiers and sequents in the HOL logic can all be lifted to operate on predicates. The lifted logical operators and sequents form a Logic of Predicates (LP) whose behavior resembles closely that of the unlifted HOL logic. Of the applications of LP we describe two in some detail: (1) ...

We present a non-commutative linear logic | the logic of predicates with equality and explicit substitutions. Thus, the position of linear logic with respect to the usual logic is given a new explanation. 1 The world according to Girard A recent introduction to linear logic, cf. 13], starts with the following explanation of the position of usual logic with respect to the linear. Linear logic is...

Linear logic presents a unified framework for describing and reasoning about stateful systems. Because of its view of hypotheses as resources, it supports such phenomena as concurrency, external and internal choice, and state transitions that are common in such domains as protocol verification, concurrent computation, process calculi and games. It accomplishes this unifying view by providing lo...

Abstract Predicate intuitionistic logic is a well-established fragment of dependent types. Proof construction in this logic, as the Curry–Howard isomorphism states, process program synthesis. We present automata that can handle proof and synthesis full first-order logic. Given formula, we construct an automaton such formula provable if only has accepting run. As further research, makes it possi...

Subexponential logic is a variant of linear logic with a family of exponential connectives—called subexponentials—that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that a classical propositional multiplicative subexponential logic (MSEL) with one unrestricted and two linear subexponentials can en...

Relation-changing modal logics are extensions of the basic modal logic that allow to change the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add and swap edges in the model, both locally and globally. We investigate the satisfiability problem of these logics. We define satisfiability-prese...

This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to think of probability as a modal operator. Contrary to popular belief in AI, a probability ranging between 0 and 1 represents a continuum between impossibility a...

We introduce a new semantics for modal predicate logic, with respect to which a rich class of first-order modal logics is complete, namely all normal first-order modal logics that are extensions of free quantified K. This logic is defined by combining positive free logic with equality PFL . = and the propositional modal logic K. We then uniformly construct—for each modal predicate logic L—a can...