Paraconsistent logic

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

Intelligent paraconsistent logic controller and autonomous mobile robot emmy II

Abstract: In this work we present a logic controller based on Paraconsistent Annotated Logic named Paracontrol, which can be applied to resolve conflicts and to deal with contradictions and/or paracompleteness, by implementing a decision-making in the presence of uncertainties Such controller was implemented in a real autonomous mobile robot Emmy II

Power systems outage possibilities analysis by Paraconsistent Logic

Abstract: Para-consistent Logic is a non-classic logic whose foundations allow for the contradictions treatment without invalidating the conclusions. Several researches have been demonstrating that through algorithms named PANs - Paraconsistent Analysis Nodes is possible to establish equations determined through signals representing restrictions, risks and configurations of electric power systems networks. In this paper we presented a model with this logic where each electric power grid component is modeled to create a Net of Analysis capable to offer a risk degree for analysis and diagnosis. In that way the model offers a diagnosis and the optimal restorative strategy proposition to the electrical power after an outage. The Paraconsistent logic type used for the models is the Annotated Paraconsistent Logic (APL). The APL utilization brings certain advantages in comparison with the classic logic because allow to manipulate contradictory signals, and like this presenting a faster and reliable action to decision in some situations where the information can be vague, ambiguous or inconsistent. This method is being validated through off-line tests applied at the Eletropaulo- Eletricidade de Sao Paulo, subtransmission power system. Eletropaulo is an electric power distribution utility of Sao Paulo state, in Brazil. The results demonstrate that the Paraconsistent Logic, with their algorithms and the PANs - Para-consistent Analysis Nodes, opens a wide field for researches and developments and can be used with promising results for implementations of applied Expert Systems in analysis and electric power system re-establishment after outages to several topologic possibilities.

Generalized Correspondence Analysis for Three-Valued Logics

Abstract: Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP (which is built in the $$ \{\vee ,\wedge ,\lnot \} $$ -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete analogue of LP, strong Kleene logic $$ \mathbf K_3 $$ . In this paper, we generalize these results for the negative fragments of LP and $$ \mathbf K_3 $$ , respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or $$ \mathbf K_3 $$ , but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of $$ \mathbf K_3 $$ and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic $$ \mathbf G_3 $$ and its dual $$ \mathbf DG_3 $$ (which have different interpretations of negation than $$ \mathbf K_3 $$ and LP).

How Peircean was the “‘Fregean’ revolution” in logic?

Abstract: The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912-1986) and Donald Angus Gillies. The innovations and characteristics that comprise mathematical logic and distinguish it from Aristotelian logic, according to this conception, created ex nihlo by Gottlob Frege (1848-1925) in his Begriffsschrift of 1879, and with Bertrand Russell (1872-1970) as its chief This position likewise understands the algebraic logic of Augustus De Morgan (1806-1871), George Boole (1815-1864), Charles Sanders Peirce (1838-1914), and Ernst Schr\"oder (1841-1902) as belonging to the Aristotelian tradition. The "Booleans" are understood, from this vantage point, to merely have rewritten Aristotelian syllogistic in algebraic guise. The most detailed listing and elaboration of Frege's innovations, and the characteristics that distinguish mathematical logic from Aristotelian logic, were set forth by van Heijenoort. I consider each of the elements of van Heijenoort's list and note the extent to which Peirce had also developed each of these aspects of logic. I also consider the extent to which Peirce and Frege were aware of, and may have influenced, one another's logical writings.

Paraconsistency and its relation to worldviews

Abstract: The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some stands with respect to para-consistency. It then discusses some sources of inconsistency that are specific for worldviews, and the import of the paraconsistent turn for the worldviews enterprise.