Paraconsistent logic

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

Challenges for the logic of social research: to grasp rationality, to deal with complexity

Abstract: The two Herculean tasks ‐ to define rationality, as a basis of social order, and to tackle complexity of social phenomena ‐ require harnessing potent forces and resources of logic. One needs ‘basic logic’, that is, logical calculi to have rules of correct reasonings, then methodological reflexion on the use of mathematical models in social sciences, at last some additions to basic logic. The last involve theoretical computer science to judge the power of algorithms used in modelling, and a study of practical reasoning in social interactions; such a study is provided by the theory of games and decision-making. All that jointly deserves to be called the logic of social research. 1 1. Logic, mathematical modelling, and artificial societies The theory of logic, insofar as we attain to it, is the vision and the attainment of that Reasonabless for the sake of which the Heavens and the Earth have been created. This enthusiastic belief in logic as expressed by Charles Sanders Peirce, is what Evert W. Beth referred to with the motto of his seminal study Semantic Entailment and Formal Derivability (Amsterdam, 1955). In that study Beth succeeded in grasping an essential feature of ‘that reasonabless’ which one finds in first-order logic and the accompanying metalogical reflexion. This is just a part of the idea of rationality, but a part significant enough to be taken it as the starting point of discussion. Beth’s study, inspired by some Gentzen’s idea, offers a very important logical contribution to the notion of rationality. His predicate logic system called semantic tableaux is much worth attention for it represents the most algorithmic approach in solving the problem about an inference whether it is logically correct. It is not the only system of this kind but the one which historically was the first in a chain of similar systems, and is a fitting example to represent this whole chain. The problem of whether a formula of predicate logic is logically valid can be solved in different ways. Some of them involve the guessing of premisses from which the formula in question could be deduced; this gives us opportunity to show invention, but does not guarantee success. In other strategies, 1 This paper was supported with financial means of the State [Polish] Committee for Scientific

The Classical Logic and the Continuous Logic

Abstract: AbstractThe truth value of a proposition in classical logic is either 0 or 1, where 0 stands for falsity and 1 stands for truth. In the real world, however, there exist many propositions with variable answers that are neither false nor true. In this paper, we present the continuous logic with the truth value of a proposition falling into the continuous range [0, 1], where 0 stands for complete falsity and 1 for complete truth. To compare the continuous logic with the classical logic, fistly, we define three primitive logic operators not, and, or, and several compound logic operators not-and, not-or, exclusive-or, not-exclusive-or, and implication from \([0, 1]^{n}\) to [0, 1], where n is an integer and \(n\ge 1\). Secondly, we discuss various laws and inference rules in both the classical logic and the continuous logic. We show that the continuous logic is consistent with the classic logic, and that the classical logic is simply a special case of the continuous logic.KeywordsClassical logicContinuous logicLogic operatorLogic inference

Semantics for some non-classical possibilistic logics

Abstract: Possibilistic logic was developed as an approach to automated reasoning. The standard possibilistic expressions are classical logic formulas associated with weights. Intuitionistic logic and paraconsistent logics have proved to be useful in knowledge representation, because of their constructive and inconsistent, but non-trivial nature, respectively. Possibilistic intuitionistic logic has already been defined and some of its syntactic properties have been proved. This paper continues in that direction, defining the possibilistic C

On Non-Alethic Logic

Abstract: Non-alethic logic was introduced in da Costa [3]. In this kind of logic the principles of tertium non datur and of contradiction are not valid; furthermore, nonalethic logic constitutes a generalization of both paraconsistent and paracomplete logics. Nowadays, paraconsistent and paracomplete logics constitutes an important subject among non-classical logics, being studied in many countries, especially in Brazil, Australia, Italy and the U.S.A. In this note we present one propositional system of non-alethic logic N1 and its corresponding first-order predicate system N 1 = .

Logic and Law in Biology1

Abstract: TEN years after the publication of the “Origin of Species,” Kelvin, then Sir William Thomson, threw a bomb into the camp of the apparently victorious evolutionists. “It was quite certain,” he said, “that a great mistake had been made-that British popular geology at the present time was in direct opposition to the principles of Natural Philosophy.” According to the great physicist, the rate of cooling of the earth and other physical ‘principles’ showed that our globe could not have been in a position to support life for longer than a period of from 50 to 300 million years. In his opinion, the drafts on the bank of time demanded by those who upheld uniformitarian geology and the evolution of plants and animals could not be honoured.