Modeling human conditional reasoning of the type “if p then q” containing negations poses a challenge for connectionism. An integrate-and-fire pulsed network (INFERNET) was used to model this type of conditional reasoning. This model also provides an insight on certain human limitations. The model is compared to empirical data, and classical explanations. Statistical analysis shows that the mod...

Forward chaining is an inference algorithm based on modus ponens which is widely used but unfortunately incomplete with respect to the usual boolean logic. A solution to this incompleteness is to compile the knowledge base so that forward chaining becomes complete for any base of facts. This compilation is called achievement and was so far restricted to propositional calculus. In this paper, we...

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional lo...

These lectures are based (closely) on a current (in-progress) book project. The general topic concerns truth, paradox, and logic. My aim is to motivate, advance and a defend a new approach within the family of paraconsistent approaches to transparent truth. Specifically, I aim to motivate a ‘detachment-free’ view. In short: we enjoy a transparent truth predicate in a language free of any ‘detac...

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 article, we deal with propositional calculi over a signature containing the classical implication → with the rules of modus ponens and substitution. For these calculi we consider few recognizing problems such as recognizing derivations, extensions, completeness, and axiomatizations. The main result of this paper is to prove that the problem of recognizing extensions is undecidable for e...

Abstract Boolean connexive logic is an extension of that closed under Modus Ponens and contains Aristotle’s Boethius’ theses. According to these theses (i) a sentence cannot imply its negation the sentence; (ii) if antecedent implies consequent, then consequent consequent. Such was first introduced by Jarmu?ek Malinowski, means so-called relating semantics tableau systems. Subsequently modal de...

Introduction. In this work we discuss recursive mappings between theories which preserve deducibility, negation and implication. Roughly, we prove that any two axiomatizable theories containing a small fragment of arithmetic—this can be stated precisely—are "isomorphic" by a primitive recursive function mapping sentences onto sentences which also preserves deducibility, negation and implication...

The notion of a fuzzy set, a natural extension of a classical set, was defined in 1965 by L.A. Zadeh; see [16]. Since that time, the fuzzy set theory has been deeply developed and it has influenced many fields of applications and therefore we can find results in branches like: fuzzy time series, fuzzy modeling, fuzzy graph theory and finally, the most often one fuzzy control. In general, the fu...