N. C. A. da Costa, On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4):497--510, 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to many paraconsistent logics. It cannot be applied to such logics as CLuNs (see for example [6] or LP (see for example [22] in which all formulas of the form are theorems. It cannot be applied to such logics as the one ascribed to Vasil ev in [1] or to da Costa s C i systems (see for example [11]) because there certain formulas of the form are logically equivalent to express a non defeasible denial of A##A. I tend to think that, with respect to certain applications, CLuN is superior to all such logics. CLuN enables one to deny a certain contradiction, and does not itself deny all ....

Newton C.A. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497--510, 1974. 20

....information [BdCGH97] and there have been a number of proposals for paraconsistent logics (for reviews see [EGH95, CH97, Hun98] However, developing non trivializable, or paraconsistent logics, necessitates some compromise, or weakening, of classical logic. Key paraconsistent logics such as C [dC74] achieve this by weakening the classical connectives, particularly negation. However this results in useful proof rules such as disjunctive syllogism failing, and intuitive equivalences such as :ff fi j ff fi failing. For users of logic, such as software engineers, the migration from classical ....

....in QC logic, fi is a conclusion of both f( ff fi) ffg and fff fi; ffg. QC logic is much better behaved in this respect than other paraconsistent logics. In this section, we compare QC logic with C logic and four valued logic. Below we give a presentation of C which was proposed da Costa [dC74] All the schemata in the logic C are schemata in classical logic. Definition 6.1 The logic C is defined by the following axiom schemata together with the modus ponens proof rule. ff (fi ff) ff fi) ff (fi fl) ff fl) ff fi ff ff fi fi ff (fi ff fi) ff ....

N C da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497--510, 1974.

.... of intuitionistic logic which are LFIs (logics of Formal Inconsistency) in the sense of [5] as well as paraconsistent conservative extensions of intuitionistic positive logic which enjoy the relevance properties of the logic Pac from [2] One of these logics is da Costa famous system C ([6, 5]) The intuitionistic negation is added exactly as it is usually done in intuitionistic logic: by adding a bottom element (satisfying A for every A) and de ning the strong negation of A to be A . This results, of course, with the full propositional intuitionistic logic. This logic and ....

N. C. A. da Costa, On the theory of inconsistent formal systems, Notre Dame Journal of Formal Logic 15 (1974), 497-510.

....handling inconsistent information, and there have been a number of proposals for paraconsistent logics (for a review see [Hun98] However, developing non trivializable, or paraconsistent logics, necessitates some compromise, or weakening, of classical logic. Key paraconsistent logics such as C [dC74] achieve this by weakening the classical connectives, particularly negation. However this results in useful proof rules such as disjunctive syllogism failing, and intuitive equivalences such as :ff fi j ff fi failing. An alternative, called quasi classical (or QC) logic, is to restrict the ....

N C da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497--510, 1974.

....large knowledge system evolving by acquiring new information during a reasonably long period of time almost inevitably becomes inconsistent. The real possibility that a Knowledge System contains contradictory data has stimulated an extensive search for methods of reasoning in inconsistent systems [7, 9, 11, 12, 15, 20, 22, 23, 24, 26, 28, 32]. The classical logic, unfortunately, can be of little use for reasoning with inconsistency. The problem is that for any formula F , a conjunction F :F is unsatisfiable in the classical logic, and so contradictory data make a system S trivially meaningless, since any formula OE becomes its ....

N. C. A. da Costa, On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, v. 15, 1974, 497-510.

....system. In [3] the authors used these techniques and the general framework of algebraizability, to prove that the paraconsistent logic P1 introduced by Sette in [6] is algebraizable. This is interesting because the best known paraconsistent logics, da Costa s C n ; n = 1; 2; systems (see [2]) are not algebraizable. This fact was proved by Mortensen in [5] for a shorter proof using Blok Pigozzi s theory see [4] In this paper we will give a characterization of these algebras, we will describe its free algebras and study some aspects of its lattices of congruences. Following [1] ....

da Costa, N.C.A. On the Theory of Inconsistent Formal Systems., N.D.J.S.L., 15 (1974), 497-510.

....have an effect to localize inconsistent information in a theory and serve as useful inference tools in artificial intelligence. Historically, paraconsistent logics have been developed in the area of philosophical logic [1] and a formal framework for inconsistent theories was given by da Costa [7]. Applications of paraconsistent logics to logic programming have also been investigated by several researchers. Blair and Subrahmanian [5] firstly introduced a framework of paraconsistent logic programming. They extended Fitting s three valued semantics of logic programming [11] and developed a ....

N. C. A. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15, 497-510, 1974.

....calculus to epistemic and ontological inconsistency in APC. Elements of our approach can be traced back even further to [33, 30] However, 33] does not handle inconsistency and negation at all, while [30] considers only a subset of the logic. There is also an abundance of literature (e.g. [6, 28]) describing other approaches to inconsistency. We are not discussing them here since they employ quite di erent techniques from the ones used in this paper. APC is close in spirit to the logics derived from Post and semi Post algebras [26] However, these logics do not deal with inconsistency ....

N.C.A. da Costa. On the theory of inconsistent formal systems. Notre Dame J. of Formal Logic, 15(4):497-510, October 1974.

....Heverlee, Belgium. email: arieli cs.kuleuven.ac.be Abstract We introduce a family of preferential consequence relations, defined by a simple and natural many valued semantics. These relations share many desirable properties for common sense reasoning, such as paraconsistency (da Costa, [8]) plausibility (Lehmann, 12] adaptivity (Batens, 4, 5] and rationality (Lehmann and Magidor, 13] 1 Introduction Preferential reasoning [21] is a well known formalism for making inferences, based on the idea that in order to draw conclusions from a given theory one should not consider ....

....is that their underlying preference criteria are based on modular partial orders . We show that this property enables a robust construction of consequence relations, in the sense that such relations may be plausibility logics [12] with adaptive capabilities [4, 5] Moreover, many paraconsistent [8] consequence relations that are definable within our framework are the same as classical logic w.r.t. consistent theories. This allows us to consider formalisms that draw classical conclusions from consistent theories, and make non trivial conclusions from inconsistent ones. 1 2 Preliminaries ....

N.C.A.da-Costa. On the theory of inconsistent formal systems. Notre Damm Journal of Formal Logic 15, pages 497--510, 1974.

....logic: This logic also has both T and as designated. In addition to the 3 basic connectives above it has one extra implication connective oe. It is defined as follows: a oe b = T a = F b otherwise The truth table for this connective was first introduced in [OdC] and used also in [dC]. The corresponding logic was investigated and axiomatized in [Av3] where it is shown to be a maximal paraconsistent logic (i.e. a logic in which contradictions do not imply everything) For obvious reasons, all these systems take T as designated and none takes F . This leads into two main ....

....It is important to note that despite the last proposition classical logic and the basic Pac are not identical. In classical logic, e.g. contradictions entail everything. This is not the case for Pac : in general :A;A 6 Pac B. This means that Pac is paraconsistent in the sense of [dC]. 10 Moreover, the basic Pac has no logical contradictions : A Pac for no A . This entails immediately (since we have an internal conjunction in the language) that no 10 The relations between paraconsistent logics and many valued logics in general are studied, e.g. in [dCA] and [Se] 16 ....

da-Costa N.C.A., Theory of Inconsistent Formal Systems, Notre Dame Journal of Formal Logic, vol 15 (1974), pp. 497-510.

No context found.

da Costa, N. C. A., 'On the theory of inconsistent formal systems', Notre Dame Journal of Formal Logic XV (4), 1974, pp. 497-510.

No context found.

N. C. A. da Costa, On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4):497--510, 1974.

No context found.

N. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497--510, 1974.

No context found.

N. C. A. da Costa, "On the theory of inconsistent formal systems," Notre Dame Jour- nal of Formal Logic 11, pp.497--510, 1974.

No context found.

N. C. A. Da Costa. On the Theory of Inconsistent Formal System. Notre Dame Journal of Formal Logic, 15 (4):497-510, 1974.

No context found.

N. C. A. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4):497--510, 1974.

No context found.

N. C. A. Da Costa. On the Theory of Inconsistent Formal System. Notre Dame Journal of Forma Log i c, 15 (4):497--510, 1974.

No context found.

N. C. A. da Costa, On the theory of inconsistent formal systems, Notre Dame Journal of Formal Logic 15 (1974), 497-510.

No context found.

Da Costa, N. C. A. 1974 \On the theory of inconsistent formal systems", Notre Dame Journal of Formal Logic 15:497-510. 15

No context found.

N.C.A. da Costa. On the Theory of Inconsistent Formal Systems,Notre Dame Journal of Formal Logic 15(4):497--510, 1974.

No context found.

N.C.A. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4):497--510, 1974.

No context found.

N C da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497--510, 1974.

No context found.

da Costa, N.C.A. `On the Theory of Inconsistent Formal Systems.' Notre Dame Journal of Formal Logic, 15. 1974.

No context found.

da Costa, Newton C.A.: On the theory of inconsistent formal system, Notre Dame Journal of Formal Logic , v. 11, pp. 497-510 (1974).

No context found.

da-Costa N.C.A., Theory of Inconsistent Formal Systems, Notre Dame Journal of Formal Logic, vol 15 (1974), pp. 497-510.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC