In this paper we show that it is possible to eliminate inverse roles and functional restrictions from ALCFI knowledge bases, while preserving the soundness and completeness of inference. Specifically, we present two polynomial encodings, the first from ALCFI knowledge bases intoALCI ones, and the second fromALCI knowledge bases into ALC ones. These encodings eliminate functional restrictions an...

The interpretations of conditionals and conditional inference are often disputed. The classic logic conditional called material implication can easily be proven to be invalid, and the conditional inference rule Modus Ponens represents a tautology that becomes invalid in the face of contrary evidence from realistic scenarios. The foundations of conditionals and conditional inference seem plagued...

Abstract In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts which principle is obviously unacceptable (weak permission understood as an absence prohibition) uncontroversially valid (strong within systems with a closed repertoire situations), concentrate on for explicit per...

A rough set logic based on Heyting-Brouwer algebras HBRSL is proposed as a basis for reasoning about rough information. It is an extension of Düntsch’s logic with intuitionistic implication, and is seen as a variant of HeytingBrouwer logic. A Kripke semantics and natural deduction for the logic are presented and the completeness theorem is proved.

The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are descri...

Conditional logic is a sub-discipline of philosophical logic. It aims to provide an alternative account of conditionals in contrast to the traditional material implication analysis. The present thesis focuses on a specific possible worlds semantics for conditional logics, the Chellas-Segerberg (CS) semantics (Chellas, 1975; Segerberg, 1989), which has not been widely investigated, save by Nejdl...

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen cate...

The results presented in this paper were born in the framework of basic logic, a new logic aiming at the uniication of several logical systems. The rst result is a sequent formulation for orthologic which allows to use methods of proof theory in quantum logic. Such formulation admits a very simple procedure of cut-elimination and hence, because of the subformula property, also a method of proof...

We present the logic of bunched implications, BI, in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication, and may be viewed as a merging of intuitionistic logic and multiplicative, intuitionistic linear logic. The predi...

deviding both the subjects and the predicates of the categorical propositions into actuality and verity, afzal al-din khunaji states the actuality-parts as adjectives, but verity-parts in three forms: as simple, as relational and as conditional. since the adjectives are formulated in modern logic by conjunction, we can formulate actuality-parts as conjunctions. verity-parts can be formulated at...