In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsist...

By weakening an inference rule satisfied by logic daC, we define a new paraconsistent logic, which is weaker than logic \ and G′ 3, enjoys properties presented in daC like the substitution theorem, and possesses a strong negation which makes it suitable to express intutionism. Besides, daC ' helps to understand the relationships among other logics, in particular daC, \ and PH1.

Recently, Brass and Dix showed 143–165) that the well founded semantics WFS can be defined as a confluent calculus of transformation rules. This led not only to a simple extension to disjunctive programs 167–213), but also to a new computation of the well-founded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LP-systems CS . Such a system CS is a (...) rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: most of the well-known semantics are induced by confluent LP-systems , there are many more transformation rules that lead to confluent LP-systems , semantics induced by such systems can be used to model aggregation , the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics. (shrink)

We propose an extension of answer sets, that we call safe beliefs, that can be used to study several properties and notions of answer sets and logic programming from a more general point of view. Our definition, based on intuitionistic logic and following ideas from D. Pearce [Stable inference as intuitionistic validity, Logic Programming 38 79–91], also provides a general approach to define several semantics based on different logics or inference systems. We prove that, in particular, intuitionistic logic can be (...) replaced with any other proper intermediate logic without modifying the resulting semantics. We also show that the answer set semantics satisfies an important property, the “extension by definition”, that can be used to construct program translations. As a result we are able to provide a polynomial translation from propositional theories into the class of disjunctive programs. (shrink)