A genuine fuzzy approach to fuzzy mathematics consists in constructing axiomatic theories over suitable systems of formal fuzzy logic. The features of formal fuzzy logics (esp. the invalidity of the law of contraction) entail certain differences in form between theories axiomatized in fuzzy logic and usual theories known from classical mathematics. This paper summarizes the most important diffe...

We apply the sequents approach to the analysis of several logics derived from linear logic In particular we present a uniform formal system for Linear Logic Elementary Linear Logic and Light Linear Logic

Controlled natural languages have been used to enable the direct translation from natural language specifications into a formal description. In this abstract we make a case for such an approach to write contracts, and translating into a temporal deontic logic. Combining both temporal behaviour and deontic behaviour is challenging both from a natural language and a formal logic perspective. We p...

We define a graphical language for expressing timed requirements on concurrent systems. This formal language, called Timed Graphical Interval Logic (TGIL), is inspired by realtime extensions of Dillon’s et al Graphical Interval Logic and can be used as an alternative to timed extensions of temporal logic. We define the semantics of TGIL as a set of timed traces—using a dense time semantics—and ...

In this paper, we develop a specific formal logic in which the basic connective is fuzzy equality and the implication is derived from the latter. Moreover, the fusion connective (strong conjunction) is noncommutative. We call this logic EQ-logic. First, we formulate the basic EQ-logic which is rich enough to enjoy the completeness property. Furthermore, we introduce two extensions which seem to...

The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results insights developed in the algebraic theory of modal logic, is based on idea that Pawlak’s original approximation spaces can be seen as special instances enriched formal contexts, i.e. relational structures formal; contexts

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic ep...

Fuzzy logic is analyzed from the point of view of formal logic; the underlying calculi and their properties are surveyed.

Theorem provers are used extensively for veriication of software and hardware. While formal veriication is a mature area of research, with a growing industrial intake, it is still limited by the practical diiculty of modelling large representational systems in low-level mathematical notations. Computations involve change: to values assumed by variables, to bits stored in particular memory locat...

Our first deductive system expresses relationships between classes of things. Each class is represented by a noun naming the class, or by an adjective that describes a property that distinguishes the members of the class from nonmembers. These nouns or adjectives denoting classes of things are called categorical terms, or simply terms. For example, the term animals refers to the class of things...