Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Paraconsistent Machines and their Relation to Quantum Computing

Abstract: We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering classical logic as the underlying logic. By substituting in such theories the underlying logic by a paraconsistent logic we define a new computation model, the paraconsistent Turing machine. This model allows a partial simulation of superposed states of quantum computing. Such a feature allows the definition of paraconsistent algorithms which solve (with some restrictions) the well-known Deutsch's and Deutsch-Jozsa problems. This first model of computation, however, does not adequately represent the notions of entangled states and relative phase, which are key features in quantum computing. In this way, a more sharpened model of paraconsistent Turing machines is defined, which better approaches quantum computing features. Finally, we define complexity classes for such models, and establish some relationships with classical complexity classes.

Logic in Religious Discourse

Abstract: "Knocking on Heaven's Door" is the oldest human dream that seems unrealised still. Religious discourse does show the road, but it requires a blind faith in return. In this book logicians try to hear Heaven's Call and to analyse religious discourse. As a result, the notion of religious logic as a part of philosophical logic is introduced. Its tasks are to construct consistent logical systems formalising religious reasoning that at first sight seems inconsistent (this research is fulfilled within the limits of modal logic, paraconsistent logic and many-valued logic), to carry out an illocutionary analysis of religious discourse (this research is fulfilled in frames of illocutionary logics), and to formalise Ancient and Medieval logical theories used in the theology of an appropriate religion (they could be studied within the limits of unconventional logics, such as non-monotonic logics, non-well-founded logics, etc.).

Postulates for Paraconsistent Reasoning and Fault Tolerant Logic Programming

Abstract: In this paper we examine, from an abstract point of view, a number of properties to be satisfied not only by formalisms for paraconsistent reasoning, but also for formalisms that aim to improve on logic programming by warranting the existence of models.

Deduction Normalization Theorem for Sette’s Logic and Its Modifications

Abstract: In this paper we formulate natural deduction systems for Sette’s three-valued paraconsistent logic P1 and some related logics. For presented calculi we prove the soundness, completeness, and normalization theorems.