Paraconsistent logic

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

The role of consistency in empirical science

Abstract: Any inconsistent theory whose underlying logic is classical encompasses all the sentences of its own language. As it denies everything it asserts, it is useless for explaining or predicting anything. Nevertheless, paraconsistent logic has shown that it is possible to live with contradictions and still avoid the collapse of the theory. The main point of this paper is to show that even if it is formally possible to isolate the contradictions and to live with them, this cohabitation is neither desired by working scientists not desirable for the progress of science. Several cases from the recent history of physics and cosmology are analyzed.

Computational reasoning with nonclassical and paraconsistent logics

Abstract: The primary aim of this dissertation is to study the semantics of logic programming languages based on multivalued logics and paraconsistent logics. These are studied in two settings: in the first, a framework for logic programming based on a family of logics called annotated logics is proposed. Different special cases of this formalism yield methods for reasoning in the presence of (classical) inconsistency. We develop a model theory and a fixed point theory and thereby study the declarative semantics of such programs. We also develop procedures to process queries. In the second formalism, we assume that multivalued programs consist of sets of clauses each of which has an associated truth value. We then define a family of logics (and a family of logic programs based on these logics). The critical feature is that we do not commit ourselves to any specific definition of the "attenuation" function that describes how to "propagate" a truth value from the body of a clause to the head of the clause. This allows us to reason in the presence of uncertainty. Finally, we study the algebraic properties of the space of operators associated with (classical) general logic programs and later conduct a similar investigation for annotated logic programs.

Mathematics Trend of Dialectical Logic

Abstract: Firstly,the limitation of standard logic is analysed in this paperVarious demands to logics proposed by the further development of artificial intelligence are discussedand it also proposed that various kinds of non-standard logics that rise vigorously explore from different level or side on how to deal with various kinds of contradiction and uncertainty,they are probing into the mathematics way of dialectical logicSecondly,the realization of dialectical logic mathematics research planning" Research outline of universal logics"put forward by the authors is introduced briefly,and the main point of" the standard proposition universal logics" set up under the guidance of the outline is also introducedThis logic system is pointed out that while forgiving various kinds of dialectical contradictions,the system have got rid of the logical contradiction effectivelyFinally,the world universal logic research status and the 2nd World Congress on Universal Logic are introduced in the article,hoping to bring everybody's attention

Quasi-classical reasoning in paraconsistent databases

Abstract: The well-founded model for any general deductive database computed using the paraconsistent relational model, based on four-valued logic, does not support inference rules such as disjunctive syllogism. In order to support disjunctive syllogism, we utilize the generalization of the relational model to quasi-classic (QC) logic, whose inference power is much closer to classical logic. As the paraconsistent relational model is capable of representing incomplete and inconsistent data, we propose an algorithm to find QC model for inconsistent positive extended disjunctive deductive databases. We also provide the proof for the algorithm.