Abduction is usually defined in terms of classical logical consequence. In this paper we substitute this ’inferential parameter’ by the notion of strict implication. By doing so we hope to put more of the intended meaning of the abductive explanative relation into the background theory. By using strict rather than material implication static domain knowledge for abductive tasks can deal with so...

Equilibrium logic, introduced by David Pearce, extends the concept of an answer set from logic programs to arbitrary sets of formulas. Logic programs correspond to the special case in which every formula is a “rule” — an implication that has no implications in the antecedent (body) and consequent (head). The semantics of equilibrium logic looks very different from the usual definitions of an an...

For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called Mà L, is based on the finite ordinal sums of à Lukasiewicz t-norms. In addition to the usual connectives – the conjunction ̄, the implication →, and the constant 0 –, we use a further unary connective interpreted by the function associating with each truth...

The notion of parsing as deduction appears to presuppose that of grammar as logic though in fact the former has largely involved embedding grammars in logics using a fragment conducive to theorem proving It is well known that categorial grammars take the form of implicational logics in this case the grammar is not embedded but simply is is a logic The paper argues that many further operations m...

A minimal formula of a given logic L is a formula which is provable in L and is not a non-trivial substitution instance of other provable formulas in L. In [5], Y. Komori asked whether normal proofs of minimal formulas are unique in the implicational fragments of natural deduction systems for the intuitionistic logic and the logic BCK. It was already shown that the answer is positive for BCK, w...

Abstract The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that founded ancient logicians like Aristotle, Chrysippus, and Boethius; it further developed medieval Abelard, Kilwardby, Paul Venice; rediscovered the 19th twentieth century Lewis Carroll, Hugh MacColl, Frank P. Ramsey, Everett J. Nelson. From 1960 onwards, finally transformed into non-classical...

small polygroups are multi-valued systems that satisfy group-likeaxioms. using the notion of “belonging ($epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy subpolygroups isintroduced. the study of ($epsilon$, $epsilon$ $vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. characterization and some of the fundam...

Adequate coverage is one of the main problems for distributed wireless sensor networks and The effectiveness of that highly depends on the sensor deployment scheme. Given a finite number of sensors, optimizing the sensor deployment will provide sufficient sensor coverage and save power of sensors for movement to target location to adequate coverage. In this paper, we apply fuzzy logic system to...

An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inferenc...

We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unifie...