Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the E...

We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic. Specifically, we consider a first-order fuzzy predicate logic alongwith its modal fragment, and show that the fuzzy first-order formulas that are non-expansive w.r.t. the natural notion of bisimulation distance are ex...

Decidability of the validity problem is established for a family of many-valued modal logics, notably modal logics based on Gödel logics, where propositional connectives are evaluated locally at worlds according to the order of values in a complete sublattice of the real unit interval, and box and diamond modalities are evaluated as infima and suprema of values in (many-valued) Kripke frames. W...

This note presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic Linear Logic wi...

Abstract Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal potential any such language, allowing us realize that vast class noun phrases, including non-denoting terms, be accommodated in new as expressions suited being subjects sentences. In light this, formal sys...

In the present paper we study systematically several consequence relations on the usual language of propositional intuitionistic logic that can be defined semantically by using Kripke frames and the same defining truth conditions for the connectives as in intuitionistic logic but without imposing some of the conditions on the Kripke frames that are required in the intuitionistic case. The logic...

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...

We present proof-theoretical and semantical characterizations of two multi-agent deontic logics for dealing with normative conflicts. The resulting logics PMDL and PMDL are non-standard in at least two respects. First, they are nonclassical in the sense that they invalidate some inferences of the propositional fragment of Classical Logic (CL). Consequently, they also invalidate certain inferenc...

Non-commutative logic, which is an uniication of commutative linear logic and cyclic linear logic, is extended to all linear connectives: additives, exponentials and constants. We give two equivalent versions of the sequent calculus | directly with the structure of series-parallel order varieties, and with their presentations as partial orders |, phase semantics and a cut elimination theorem.