References [Table of contents]
|
[Bat80] [bibitem] Diderik Batens. Paraconsistent extensional propositional logics. Logique et Analyse, 90-91:195-234, 1980. [scan] |
| A philosophical and technical study of a set of propositional paraconsistent logics that extends a basic system, here called PI. Its predicative extension, CLuN, is studied in [Bat99b] and elsewhere. This system, seems to lead to the most efficient inconsistency-adaptive logic for applications in the philosophy of science. |
|
[Bat87] [bibitem] Diderik Batens. Relevant implication and the weak deduction theorem. Studia Logica, 46:239-245, 1987. |
| A Tarski-like characterization of the pure logic of relevant implication. |
|
[Bat02c] [bibitem] Diderik Batens. On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics. In Carnielli et al. [CCLD02], pages 275-293. [scan] |
|
Abstract This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL. Three kinds of connections are illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest's LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another. The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person's semantics for S5 as well as a description of the simple but useful and powerful AL. |
|
[Bat06a] [bibitem] Diderik Batens. A diagrammatic proof search procedure as part of a formal approach to problem solving. In Magnani [Mag06], pages 265-284. [ps.zip] [pdf] |
|
Abstract This paper aims at describing a goal-directed and diagrammatic method for proof search. The method (and one of the logics obtained by it) is particularly interesting in the context of formal problem solving. A typical property is that it consists of attempts to justify so-called bottom boxes by means of premise elements (diagrammatic elements obtained from premises) and logical elements. Premises are not preprocessed, whence most premises lead to a variety of premise elements. |
|
[Batar] [bibitem] Diderik Batens. A poor person’s semantics for modal logics. To appear. (zipped) |
|
Abstract The two semantic systems presented in this paper are characteristic of S5. The first proceeds in terms of a set of models for Classical Logic, the second in terms of a slightly extende language combined with one such model. The intuitive interpretation is attractive and the metatheoretic proofs simple. At the expense of some complication, the method may be adapted to other modal logics. |
|
[BDCng] [bibitem] Diderik Batens and Kristof De Clercq. Embedding and interpolation for some paralogics. The predicative case. Forthcoming. |
| Extension of [BDCK99] to the predicative case. |
|
[BDC04] [bibitem] Diderik Batens and Kristof De Clercq. A rich paraconsistent extension of full positive logic. Logique et Analyse, 185-188:227-257, 2004. Appeared 2005. [ps.zipped] |
|
Abstract In the present paper we devise and study the most natural predicative extension of Sch\"{u}tte's maximally paraconsistent logic. With some of its large fragments, this logic, \sys{CLuNs |
| This paraconsistent logic seems especially useful as a lower limit logic for inconsistency-adaptive logics that are suitable for mathematical contexts. |
|
[BDCK99] [bibitem] Diderik Batens, Kristof De Clercq, and Natasha Kurtonina. Embedding and interpolation for some paralogics. The propositional case. Reports on Mathematical Logic, 33:29-44, 1999. [scan] |
|
Abstract We consider the very weak paracomplete and paraconsistent logics that are obtained by a straightforward weakening of Classical Logic, as well as some of their maximal extensions that are a fragment of Classical Logic. We prove (for the propositional case) that these logics may be faithfully embedded in Classical Logic (as well as in each other), and that the interpolation theorem obtains for them. |
| Helpful to obtain more control on the computational aspects of adaptive logics that have those paralogics as their lower limit logic. |
|
[BDP97] [bibitem] Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17-45, 1997. |
| All these flat Rescher--Manor consequence relations are characterized by inconsistency-adaptive logics in [Bat00d] and by (modal) ampliative adaptive logics in [Bat03b]. |
|
[BDP99] [bibitem] Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Orlowska [Orl99], pages 473-511. |
| All these prioritized Rescher--Manor consequence relations are characterized by by (modal) ampliative adaptive logics in [Ver03b]. |
|
[BS98] [bibitem] Philippe Besnard and Torsten Schaub. Signed systems for paraconsistent reasoning. Journal of Automated Reasoning, 20:191-213, 1998. |
|
[BJ89] [bibitem] George S. Boolos and Richard J. Jeffrey. Computability and Logic. Cambridge University Press, 1989. (Third edition). |
|
[BBJ02] [bibitem] George S. Boolos, John P. Burgess, and Richard J. Jeffrey. Computability and Logic. Cambridge University Press, 2002. (Fourth edition). |
|
[dCBF98] [bibitem] Newton C.A. da Costa, Otávio Bueno, and Steven French. The logic of pragmatic truth. Journal of Philosophical Logic, 27:603-620, 1998. |
| Relies on [MdCC86] and [Jas69]. |
|
[HH05] [bibitem] Ilpo Halonen and Jaakko Hintikka. Toward a theory of the process of explanation. Synthese, 143:5-61, 2005. |
|
[Ja{\'{s}}69] [bibitem] Stanislaw Jaskowski. Propositional calculus for contradictory deductive systems. Studia Logica, 24:243-257, 1969. |
| First English phrasing of discussive logic. Jaskowski and da Costa were the first to devise decent paraconsistent logics. |
|
[MdCC86] [bibitem] Irene Mikenberg, Newton C. A. da Costa, and Rolando Chuaqui. Pragmatic truth and approximation to truth. Journal of Symbolic Logic, 51:201-221, 1986. |
| Technical study of pragmatic truth. This notion is approached by techniques inspired by [Jas69]. |
|
[Nas03] [bibitem] Marek Nasieniewski. The axiom of McKinsey-Soboci\’nski K1 in the framework of discussive logics. Logique et Analyse, 183-184:315-324, 2003. Appeared 2005. |
|
Abstract In this paper we use Ja{\'{s}}kowski's method of defining a propositional logic with the help of the M-fragment of a given modal logic to express classical logic. We use as weak tools as possible to do this. A strengthening of some results by Scott and Lemmon concerning the McKinsey-Soboci{\'{n}}ski axiom is presented. This paper is a part of the investigation of building the adaptive logic on the basis of the logic D2. |
|
[Rahar] [bibitem] Shahid Rahman. From games to dialogues and back. Towards a general frame for valitity. To appear. |
| ZOEKEN |
|
[Res64] [bibitem] Nicholas Rescher. Hypothetical Reasoning. North-Holland, Amsterdam, 1964. |
| Basic source for [BDP97] and [BDP99]. |
|
[Res76] [bibitem] Nicholas Rescher. Plausible Reasoning. An Introduction to the Theory and Practice of Plausibilistic Inference. Van Gorcum, Assen/Amsterdam, 1976. |
| Basic source for [BDP97] and [BDP99]. |
|
[RM70] [bibitem] Nicholas Rescher and Ruth Manor. On inference from inconsistent premises. Theory and Decision, 1:179-217, 1970. |
| Basic source for [BDP97] and [BDP99]. |