Paraconsistent logic

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

Dualising Intuitionictic Negation

Abstract: One of Da Costa's motives when he constructed the paraconsistent logic Cw was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to CWo Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature 'Brouwerian logic' or 'closed-set logic'.

Statistics of Intuitionistic versus Classical Logics

Abstract: For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see [2]). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.

Paraconsistent Reasoning for Expressive and Tractable Description Logics

Abstract: Four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases, mainly ALC This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as classical semantics In this paper, we further study how to extend the four-valued semantics to more expressive description logics, such as SHIQ, and to more tractable description logics including EL++, DL-Lite, and Horn-DLs The most effort we spend defining the four-valued semantics of expressive four-valued description logics is on keeping the reduction from four-valued semantics to classical semantics as in the case of ALC; While for tractable description logics, we mainly focus on how to maintain their tractability when adopting four-valued semantics

A first-order, four valued, weakly paraconsistent logic and its relation to rough sets semantics

Abstract: A first order four-valued logic, called DDT, is presented in the paper as an extension of Belnap’s logic using a weak negation and establishing an appropriate semantic for the predicate calculus. The logic uses a simple algebraic structure, that is the smallest non trivial interlaced bilattice on the four truth values, thus resulting in a boolean algebra on the set of truth values. The logic is a language for reasoning under uncertainty, enabling to capture hesitation due either to inconsistent or incomplete information, while keeping a clear distinction between these epistemic states. The logic was originally developed for preference modelling purposes (for which a brief account is given in the paper). The paper demonstrates and discusses the equivalence between the semantics of this logic and of rough sets semantics. On this basis, this papers presents the possibility of inducing rules from examples, that can be integrated in systems whose inference is expressed in the above logic. Such an approach enhances the potentialities of the use of rough sets in classification, reasoning and decision support.