Paraconsistent logic

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

What is a logical system

Abstract: 1. What is logic 2. Logic without model theory 3. Diagrams and the concept of logical system 4. General dynamics 5. What is a deductive system 6. The transmission of truth and the transmitting of abduction 7. What is a logical system? 8. What is a logical system? 9. Structure, consequence relation 10. Schematic consequence 11. Logical constants and punctuation marks 12. Finitary inductively presented logics 13. A-theory and its metatheory in FSo 14. General logics and logical frameworks 15. General algebraic logic, a perspective on What is Logic?

Constructive Negations and Paraconsistency

Abstract: Reductio ad Absurdum.- Minimal Logic. Preliminary Remarks.- Logic of Classical Refutability.- The Class of Extensions of Minimal Logic.- Adequate Algebraic Semantics for Extensions of Minimal Logic.- Negatively Equivalent Logics.- Absurdity as Unary Operator.- Strong Negation.- Semantical Study of Paraconsistent Nelson's Logic.- N4?-Lattices.- The Class of N4?-Extensions.- Conclusion.

Rules of definitional reflection

Abstract: The author discusses two rules of definitional reflection: the logical version of definitional reflection, as used in the extended logic programming language GCLA, and the omega version of definitional reflection. The logical version is a left-introduction rule completely analogous to the left-introduction rules for logical operators in Gentzen-style sequent systems, whereas the omega version extends the logical version by a principle related to the omega rule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection. >

General logical databases and programs: default logic semantics and stratification

Abstract: Default logic is introduced as a well-suited formalism for defining the declarative semantics of deductive databases and logic programs. After presenting, in general, how to use default logic in order to define the meaning of logical databases and logic programs, the class of stratifiable databases and programs is extensively studied in this framework. Finally, the default logic approach to the declarative semantics of logical databases and programs is compared with the other major approaches. This comparison leads to showing some advantages of the default logic approach.

Paraconsistent Logics and Paraconsistency

Abstract: Publisher Summary This chapter discusses paraconsistent logics (PL) and paraconsistency. PL are the logics of inconsistent but nontrivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well-formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. In a trivial theory “everything” (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems such as intuitionistic logic, inconsistency entails triviality, and conversely. This chapter discusses da Costa's C-logics. This chapter elaborates on paraconsistent set theories, and shows, in particular, how they accommodate inconsistent objects, such as the Russell set. Ja´skowski's discussive logic is examined, and it is showed how it can be used in the formulation of the concept of partial truth. The chapter also examines annotated logic, and some of its applications.