Paraconsistent logic

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

Modeling Paraconsistent Reasoning by Classical Logic

Abstract: We introduce a general method for paraconsistent reasoning in knowledge systems by classical second-order formulae. A standard technique for paraconsistent reasoning on inconsistent classical theories is by shifting to multiple-valued logics. We show how these multiple-valued theories can be "shifted back" to two-valued classical theories (through a polynomial transformation), and how preferential reasoning based on multiple-valued logic can be represented by classical circumscription-like axioms. By applying this process we manage to overcome the shortcoming of classical logic in properly handling inconsistent data, and provide new ways of implementing multiple-valued paraconsistent reasoning in knowledge systems. Standard multiple-valued reasoning can thus be performed through theorem provers for classical logic, and multiple-valued preferential reasoning can be implemented using algorithms for processing circumscriptive theories (such as DLS and SCAN).

Two aspects of relevance in structured argumentation: minimality and paraconsistency

Abstract: This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC+ framework, arising from the combined use of strict and defeasible inference rules. One issue arises if the strict inference rules correspond to classical logic. A longstanding problem is how the trivialising effect of the classical Ex Falso principle can be avoided while satisfying consistency and closure postulates. In this paper, this problem is solved by disallowing chaining of strict rules, resulting in a variant of the ASPIC+ framework called ASPIC*, and then disallowing the application of strict rules to inconsistent sets of formulas. Thus in effect Rescher & Manor's paraconsistent notion of weak consequence is embedded in ASPIC*. Another issue is minimality of arguments. If arguments can apply defeasible inference rules, then they cannot be required to have subset-minimal premises, since defeasible rules based on more information may well make an argument stronger. In this paper instead minimality is required of applications of strict rules throughout an argument. It is shown that under some plausible assumptions this does not affect the set of conclusions. In addition, circular arguments are in the new ASPIC* framework excluded in a way that satisfies closure and consistency postulates and that generates finitary argumentation frameworks if the knowledge base and set of defeasible rules are finite. For the latter result the exclusion of chaining of strict rules is essential. Finally, the combined results of this paper are shown to be a proper extension of classical-logic argumentation with preferences and defeasible rules.

Metareasoning for multi-agent epistemic logics

Abstract: We present an encoding of a sequent calculus for a multi-agent epistemic logic in Athena, an interactive theorem proving system for many-sorted first-order logic. We then use Athena as a metalanguage in order to reason about the multi-agent logic an as object language. This facilitates theorem proving in the multi-agent logic in several ways. First, it lets us marshal the highly efficient theorem provers for classical first-order logic that are integrated with Athena for the purpose of doing proofs in the multi-agent logic. Second, unlike model-theoretic embeddings of modal logics into classical first-order logic, our proofs are directly convertible into native epistemic logic proofs. Third, because we are able to quantify over propositions and agents, we get much of the generality and power of higher-order logic even though we are in a first-order setting. Finally, we are able to use Athena's versatile tactics for proof automation in the multi-agent logic. We illustrate by developing a tactic for solving the generalized version of the wise men problem.

Possible-translations algebraization for paraconsistent logics

Abstract: This note proposes a new notion of algebraizability, which we call possibletranslations algebraic semantics, based upon the newly developed possibletranslations semantics. This semantics is naturally adequate to obtain an algebraic interpretation for paraconsistent logics, and generalizes the well-known method of algebraization by W. Blok and D. Pigozzi. This generalization obtains algebraic semantics up to translations, applicable to several non-classical logics and particularly apt for paraconsistent logics, a philosophically relevant class of logics with growing importance for applications.

Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum Factor of Quantization hψ

Abstract: We present in this paper an alternative of modeling physical systems through a non-Classical logic namely the Paraconsistent Logic (PL) whose main feature is the revocation of the principle of non-contradiction. The Paraconsistent Annotated Logic with annotation of two values (PAL2v) is a type of PL and has in its theoretical structure the main feature of dealing with contradictions offering flexibility in drawing conclusions. Several works about applications of PAL2v have shown that such logic is able to provide us with an adequate treatment to uncertainties. Based on the foundations of the PAL2v we presented the ParaQuantum logic (PQL) with the goal of performing analysis of signals from information sources which model physical systems. The formalization of the concepts of the logics PQL, that it is represented in a Lattice, requires the considering of Paraquantum logical states ψ which are propagated through variations of the evidence Degrees µ and λ which come out from measurements performed in Observable Variables in the physical world. When we analyze the lattice of the PQL, we obtain equations which quantify values of physical quantities from where we obtain the effects of propagation of the Paraquantum logical states ψ. In this paper, we introduce the Paraquantum Factor of quantization hψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. We conclude through these studies that the Paraquantum Logical Model based on the ParaQuantum logics PQL can link the several fields of the physical sciences by means of quantization of values. It is an innovative approach of formulating natural phenomena.