Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....obtained by stipulating that A is an R consequence of a default theory T i# #A is a T consequence of the modal translation of T . The system T is an adaptive logic. The first adaptive logic was designed by Diderik Batens around 1980 and was meant to handle inconsistent theories (see [2]) Later, the notion of an adaptive logic was generalized to include other types of logical abnormalities (negation incompleteness, for instance) and several non monotonic consequence relations were reconstructed in terms of adaptive logics (see, for instance, 4] and [11] A more recent ....

D. Batens. Dynamic dialectical logics. In G. Priest, R. Routley, and J. Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....both Q refer to specific logics of questions, the mechanism by which they are obtained may easily be applied to other logics of questions. The techniques that led to Q derive from the adaptive logic programme. The first adaptive logic was designed by Diderik Batens around 1980 (see [1]) Meanwhile, a whole variety of such logics is available see [2] and [4] for a survey. As we shall see below, the importance of adaptive logics is that they enable one to study, in a formally exact way, reasoning patterns that are non monotonic and or dynamic. Other types considered by ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....test. Hence, if A, there is bound to exist a CL proof of A from #, even if we may never find it. at that moment, the best possible estimate of which conclusions are derivable from the premises. 4 Adaptive Logics The first adaptive logic was designed around 1980 by Diderik Batens (see [2] and [4] and was meant to handle in a sensible and realistic way inconsistent sets of premises. This logic was followed by several other inconsistency adaptive systems (see, for instance, 61] 44] and [51] and several inconsistency handling mechanisms that proceed in terms of maximal ....

....invalidate rules of inference, but only specific applications of such rules. As follows from the above description, P is a corrective system. Hence, its upper limit logic is CL. Its lower limit logic is P full positive logic plus A##A, was first presented at the propositional level in [2], and extended to the predicative level in [4] a tableau method for this logic can be found in [18] and [20] In many papers on the subject, the logic is called ACLuN1 . and its set of abnormalities# #(A # #A) Note that extending P with the presupposition that all members of# are false ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....of questions, it is important to note that the mechanism by which they are obtained may easily be applied to other logics of questions. The techniques that led to Q and Q derive from the adaptive logic programme. The first adaptive logic was designed by Diderik Batens around 1980 (see [1]) Meanwhile, a whole variety of such logics is available see [3] and [5] for a survey. As we shall see below, the importance of adaptive logics is that they enable one to study in a formally exact way reasoning patterns that are non monotonic and or dynamic. I shall proceed as follows. After ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....in favour of H # . Importantly, this withdrawal is governed by the logic itself, and hence, does not depend on a decision of the user. The techniques that led to the logic LA k derive from the adaptive logic programme. The first adaptive logic was designed by Diderik Batens around 1980 (see [2]) and was meant to handle in a sensible and realistic way inconsistent sets of premises. This logic was followed by other inconsistency adaptive systems (see, for instance, 19] and [14] and the idea of an adaptive logic was generalized to other forms of logical abnormalities, such as ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....a satisfactory way may take several years. In the meantime, however, these knowledge systems and theories are used to generate explanations. 2 The techniques that led to CP1 and CP2 derive from the adaptive logic programme. The first adaptive logic was designed around 1980 by Diderik Batens (see [2]) and was meant to handle in a sensible and realistic way inconsistent sets of premises. This logic was followed by several other inconsistency adaptive systems (see, for instance, 33] 20] and [22] Later the idea of an adaptive logic was generalized to other forms of logical abnormalities, ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989. 22 Unpublished papers in the reference section are available at the internet address http://logica.rug.ac.be/centrum/writings. 24

....below is that they enable one to localize the consistent core of an inconsistent set #. In Section 5, we shall see how this is realized. But first, I need to explain the basic concepts of adaptive logics. 4 Adaptive Logics The first adaptive logic was designed by Diderik Batens around 1980 (see [1]) and was an inconsistency adaptive logic. As their name indicates, inconsistencyadaptive logics localize the specific inconsistencies that follow from a theory, and adapt themselves to these. If some consequences of a theory behave inconsistently, applications of the rules of inference to ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....This is as it should be. Even if two participants contradict each other, it should be possible to conjoin the statements on which they agree. The techniques that led to D2 r derive from the adaptive logic programme. The first adaptive logic was designed by Diderik Batens around 1980 (see [2]) Meanwhile, a whole variety of such logics is available see [5] for a survey. As we shall see below, the importance of adaptive logics is that they enable one to study in a formally exact way reasoning patterns that are non monotonic and or dynamic. A reasoning pattern is called dynamic if the ....

....2 Not all dynamic reasoning patterns are non monotonic. In [6] for instance, Batens shows that the pure logic of relevant implication can be characterized by a dynamic proof theory. 3 Readers familiar with adaptive logics will see that I rely on insights and proof techniques from [2], 3] 4] and [9] The proofs of Lemma 2 and Theorem 14 rely on proof techniques first presented in [3] the proof of Theorem on a technique from [4] 3 a whole variety of non classical logics was designed. Most of these are obtained by simply dropping some CL presuppositions and by restricting ....

Diderik Batens. Dynamic dialectical logics. In Priest et al. [29], pages 187--217.

....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 all the models of that theory, but only a subset of ....

....property shared by all these relations 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 ....

[Article contains additional citation context not shown here]

D.Batens. Dynamic dialectical logics. Paraconsistent Logic. Essay on the Inconsistent (G.Priest, R.Routely, J.Norman, editors), pages 187-217, Philosophia Verlag, 1989.

....of competitor from logic programming together with the conditionallity that is common in all adaptive proofs. 1 Introduction The primary aim of this article is to show that adaptivity, as it is already known in some non monotonic logics (most of them paraconsistent, cfr. Diderik Batens [1] [2] (the oldest paper) 3] and others) is also applicable in other elds, in casu logic programming. Moreover, our claim is that moving to an (inconsistency ) adaptive strategy brings along many bene ts for logic programming. The adaptive strategy has proven to be a very useful tool in all areas ....

Diderik Batens. Dynamic dialectical logics. In G. Priest, R. Routley, and J. Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187-217. Philosophia Verlag, Munchen, 1989.

....from , A occurs as the second element and fC 1 ; Cm g (0 m) occurs as the fth element of a line, then pHL A DEKfC 1 ; Cm g. 11 In view of this lemma, we can introduce the following derivation rule. 11 The proof of Lemma 2 is completely analogous to the proof of Lemma 1 in [1] and Lemma 4.2 in [4] 14 Dek: A, A DEK( Definition. A DEK consequence of is a DEK formula which is pHL derivable from . Definition. DEK( is a minimal DEK consequence of i it is a DEK consequence of , and for no , DEK( is a DEK consequence of . Theorem 8 HL A, i there ....

....It follows that A is nally derived at that line. Whence HL2 A. 2. In HL and HL1 no factor of a minimal DEK consequence is reliable. In HL2 however, those factors of a minimal DEK consequence are reliable the 22 The proof of Lemma 3 is completely analogous to the proofs of Lemma 1 in [1] and Lemma 4.2 in [4] 21 conditional preference of which is higher than the conditional preference of some other factor of that minimal DEK consequence. The marking rule mr1 of HL and HL1 is valid in HL2. I now give the typical HL2 rule concerning marking of instances. Definition: If A occurs ....

Batens, Diderik: \Dynamic Dialectical Logics", in G. Priest, P. Routley & J. Norman (eds.) Paraconsistent Logic. Essays on the Inconsistent. Munchen, pp. 187-217.

....in which C 1 ; Cm is the fth element, a new line can be added with A DEKfC 1 ; Cm g as second element and an empty fth element, and vice versa. The following Theorem expresses an important feature of HL: 11 The proof of Lemma 2 is completely analogous to the proof of Lemma 1 in [1] and Lemma 4.2 in [4] 12 The proof of Theorem 8 is completely analogous to the proof of Theorem 4.3 in [4] 14 Theorem 9 If HL A, then it is possible to extend any proof from into a proof in which A is nally derived from . 13 I now give a derivable marking rule in HL. mr1: If A (resp. ....

....two di erent preferences. Therefore we can accept that every formula has (at maximum) one conditional preference. 21 It is handy to indicate the conditional preference of the formulas in the fth column of a proof. 22 The proof of Lemma 3 is completely analogous to the proofs of Lemma 1 in [1] and Lemma 4.2 in [4] 20 Hence pHL2 A DEKfC 1 ; Cm g. pHL2 A DEKfC 1 ; Cm g (0 m) Suppose now that C i is a factor of a minimal DEK consequence D of and there is no other factor of D with a lower conditional preference than C; then there is an extension of the proof in which D ....

Batens, Diderik: \Dynamic Dialectical Logics", in G. Priest, P. Routley & J. Norman (eds.) Paraconsistent Logic. Essays on the Inconsistent. Munchen, pp. 187-217.

....A is derived. The formal marking rule can be found in [5] A formula A is said to be nally derivable from a set of 9 For an account on these two logics, see, among others, Diderik Batens [5] The rst inconsistency adaptive logic, originally called dynamic dialectical logic, can be found in [4]. 10 The rst four elements of a line in a proof are (1) the number of the line, 2) the derived formula, 3) the numbers of the lines used to derive the formula mentioned as second element, and (4) the derivation rule used. 8 premises i every proof of A from that can be extended in such a ....

Diderik Batens. Dynamic dialectical logics. In G. Priest, R. Routley, and J. Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187-217. Philosophia Verlag, Munchen, 1989.

....abnormality adaptive logic is more suitable. 3 I am extremely indebted to Diderik Batens and Kristof De Clercq, for their large amount of interesting comments on earlier versions of this paper. Research for this paper was supported by the Fund for Scienti c Research Flanders. 1 See, e.g. [1], 3] 4] 5] 2 The logics ACLuN1 and ACLuN2 are well known (see, e.g. 5] 3 [3] and especially [4] contain a plea for developing logics that are adaptive with respect to other kinds of logical abnormalities results are forthcoming. 1 The adaptive logic presented in this paper, is ....

Batens, Diderik: \Dynamic Dialectical Logics", in G. Priest, P. Routley & J. Norman (eds.) Paraconsistent Logic. Essays on the Inconsistent. Munchen, 1980, pp. 187-217.

.... (A B) A B) A (A B) A B) A (A B) A B) A B) A8 (8 )A( A( A9 A( 9 )A( A = 1 = A = 2 = A B) where B is obtained by replacing in A an occurence of by A 8 (8 )A (9 ) A A 9 (9 )A (8 ) A 2 For an account on CLuN, see [1] and [2] among others. CLuNs was rst presented in [3] In this last paper, the authors give the axiomatization, semantics and metatheory of CLuNs. Here, we only need the axioms. 2 The di erence between CLuN and CLuNs is to be found in the seven A axioms, which do not occur in the ....

Diderik Batens. Dynamic dialectical logics. In G. Priest, R. Routley, and J. Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187-217. Philosophia Verlag, Munchen, 1989.

....properties, theorems and lemmas on Batens article. 1 These inconsistencies are caused by so called informational overdetermination . 2 An inference is called hypothetical in this sense, if its antecedent premisses are i y (see [Res76] 3 See [Res76] page 80. 4 See, among others, his [Bat89], Bat98] and [Bata] 2 This paper is eesentially about argumentation from prioritized belief bases. It should be noted, however, that argumentation is perhaps not the most suitable word for the type of reasoning described here. Typically in an argumentation, there are (at least) two parties: ....

....logic, but shares with paraconsistent logics the property of not leading to triviality in the face of an inconsistency. As such, they are excellent tools for reasoning from inconsistent knowledge bases. For details on how inconsistency adaptive logics work, I refer to Diderik Batens articles [Bat89], Bat98] Bata] and [Batb] Yet, I believe it necessary to give a brief introduction to these logics here. 3.1 The paraconsistent logic CLuN The logic CLuN is a very poor, paraconsistent logic. It is poor because it is a mere weakening of CL, and it is paraconsistent because the consistency ....

Diderik Batens. Dynamic dialectical logics. In G. Priest, R. Routley, and J. Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187-217. Philosophia Verlag, Munchen, 1989.

....accepted theories that are mutually inconsistent. In still other cases, progress in a discipline was realized by reasoning from a theory and a set of data that are mutually inconsistent. The reasoning that occurs in such situations is explicated by inconsistencyadaptive logics see, for example, [3], 2] 5] 23] 14] 25] 12] 7] 8] These logics isolate the involved inconsistencies and in this way provide an interpretation of the premises (theories and or data) that is as consistent as possible. Precisely this type of interpretation is needed in order to reason from the ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....dynamic proof theory of adaptive logics. We first need a simple Lemma, the proof of which is obvious. Lemma 1 UCL is equivalent to the system obtained by restricting axioms of the form of axioma schema (1) in such a way that A # . By some historical accident, the first adaptive logics see [3], the oldest paper, and [2] were such that the lower limit logic and the upper limit logic determine a unique set of abnormalities. In this case, the set of abnormalities is a function of the lower limit logic and the upper limit logic. This caused some confusion which was only cleared up when ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....logics are obtained by interpreting a set of premises as normally as possible . As some minimal Dab consequences of # may contain more than one disjunct, this phrase is not unambiguous. It is disambiguated by choosing a specific adaptive strategy. The oldest known strategy is Reliability from [3], where it is discussed at the propositional level. Let U(#) A # for some minimal Dab consequence Dab(#) of # (the set of formulas that are unreliable on #) The Reliability strategy considers a formula as behaving abnormally i# it is a member of U(#) The e#ect of this on the semantics ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....from q. See [37] for an exception: the paraconsistent logic AN validates Disjunctive Syllogism (and all analysing rules of CL) but invalidates Addition (and Irrelevance and similar rules) Explicating this type of kind reasoning was at the origin of the adaptive logic programme see [5], 8] and many other papers. ground generalization with the data, and this will a#ect the derivability of new inductive generalizations. Often not all background generalizations will be considered equally trustworthy. So, instead of a set of background generalizations, one confronts a ....

....member of # behaves abnormally. Adaptive logics are obtained by interpreting a set of premises as normally as possible . But clearly, this phrase is not unambiguous. This is why we need to disambiguate it by choosing a specific adaptive strategy. The oldest known strategy is Reliability from [5], where it is discussed at the propositional level. Let U(#) # for some minimal Dab consequence Dab(#) of # (the set of formulas that are unreliable on #) The Reliability strategy considers a formula as behaving abnormally i# it is a member of U(#) As for the other strategies, the e#ect ....

[Article contains additional citation context not shown here]

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....(which for the present# means as consistently as possible ) but this phrase is ambiguous. As indicated in (iii) an adaptive strategy disambiguates the phrase. The oldest known strategy, and the one that is simplest from a proof theoretic point of view, is the Reliability strategy from [2]. I shall not consider any other strategies in this paper. Let Dab(#) be a minimal Dab consequence of # i# Dab(#) and there is no # # # for which # Dab(# # ) Let # for some minimal Dab consequence Dab(#) of # be the set of formulas that are unreliable with respect to #. Below, I ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....If # is normal in that it has ULL models, the AL models of # coincide with these ULL models of #. If # has no ULL models, the AL models of # are the LLL models of # that are as normal as possible . The most fascinating feature of adaptive logics is their dynamic proof theory, first presented in [2]. Characterizations in terms of consequence sets or of models may o#er precise definitions, but, unlike the dynamic proof theory, they are in themselves not computationally useful. Moreover, adaptive logics are specifically devised in order to explicate, in a formally precise way, forms of ....

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

....best insights. 2 At this point, we should mention a weakness of the Rescher Manor consequence relations. They are nicely de ned, but no clue is provided for obtaining their consequences or even a sensible estimate of them. In this respect, the adaptive logic programme see, for example, 1] [2] (the oldest paper) 4] and [5] is much more attractive: adaptive logics have a proof theory. Their proofs are dynamic: conclusions drawn at some stage of the proof may be given up at a later stage (and may again be considered as correct at a still later stage) As a result, one needs to ....

.... premises and conclusion are formalized by by the paraconsistent negation; merely functions as a technical device (introduced mainly for tableau methods and metatheoretic proofs) For many applications, the standard approach is to be preferred over the Rescher Manor consequence relations see [2] and [4] 20 DEK consequences of G that do not ful l the condition are normally derived from DEK consequences of G that do it requires a logician to derive them in a di erent way. 21 Choose M such that, for any C 2 fB 1 ; Bng, v M (C) 1 if C is a CLuN consequence of some ....

D. Batens. Dynamic dialectical logics. In G. Priest, R. Routley, and J. Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187{ 217. Philosophia Verlag, Munchen, 1989.

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Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

No context found.

Diderik Batens. Dynamic dialectical logics. In Graham Priest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187--217. Philosophia Verlag, Munchen, 1989.

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