We introduce an extension ALCQIOb,Re of the description logic ALCQIO, a sub-logic of the two-variable fragment of first order logic with counting quantifiers, with reachability assertions. ALCQIOb,Reformulae can define an unbounded number of trees. We show that finite implication of ALCQIOb,Re-formulae is polynomial-time reducible to finite satisfiability of ALCQIO-formulae. As a consequence, w...

for the first time in the history of logic, abd al razzaq al-jili (d. 570/1174), in the treatise al-lame fi al-shakl al-rabe, dealt with the modal syllogisms of the fourth figure. previous to him, dinha, the priest, and ibn salah al-hamadani had discussed the non-modal moods of the fourth figure. jili’s treatise deals only with simple modalities and ignores the complex ones. his pupil, fakhr al...

We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all element...

Abstract. Bi-intuitionistic logic is the extension of intuitionistic logic with a connective dual to implication. Bi-intuitionistic logic was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent “cut-free” sequent calculus for BiInt has recently been shown by Uustalu to fail cut-elimination. We present a new cut-free sequent calculus for BiInt, and...

We describe a new logic called typed predicate calculus (T PC) that gives declarative meaning to logic programs with type declarations and type inference. T PC supports all popular types of polymorphism, such as parametric, inclusion, and ad hoc polymorphism. The proper interaction between parametric and inclusion varieties of polymorphism is achieved through a new construct, called type depend...

For the given logical calculus we investigate the size of the proportion of the number of true formulas of a certain length n against the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit of fractions exists it represents the real number between 0 and 1 which we may call the density of truth for the...

The use of DNA molecules as a physical computational material has attracted much interest, especially in the area of DNA computing. DNAs are also useful for logical control and analysis of biological systems if efficient visualization methods are available. Here we present a quick and simple visualization technique that displays the results of the DNA computing process based on a colorimetric c...

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a “modus-ponens-like” rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication-fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set...

In this paper we present some Boolean algebras in the form of lattice by using the fuzzy implication. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature. KeywordsFuzzy logic connectives, Fuzzy implication, Algebras, Lattice.