Konolige, K. 1987. On the relation between default and autoepistemic logic. In Readings in Nonmonotonic Reasoning, M. L. Ginsberg, Ed. Kaufmann, Los Altos, CA, 195-226.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....base theory. This brief overview points to similarities in motivations and intuitions behind default and autoepistemic logics. These similarities drew attention to the issue of a formal account of the relationship between the two logics, which quickly became a subject of active research. Konolige [Kon88] proposed to translate a default ; into the autoepistemic formula: Kff :K:fi 1 : K:fi k fl: The translation was an attempt to reflect the intuition that in order to apply a default, its prerequisite must be derived and its justifications must be consistent. To model the statement ....

....default logic or that the modal reading of a default proposed by Konolige is not appropriate. Thus, researchers began to look for other modal logics and for other translations. Konolige related default logic to a version of autoepistemic logic based on the notion of a strongly grounded expansion [Kon88]. Marek and Truszczy nski [MT89b] proposed an alternative translation and represented extensions as expansions of a modal nonmonotonic logic constructed by the method of McDermott from the weakest modal logic N . Truszczy nski [Tru91] found that the Godel translation of intuitionistic logic to ....

[Article contains additional citation context not shown here]

K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35(3):343--382, 1988.

....base theory. This brief overview points to similarities in motivations and intuitions behind default and autoepistemic logics. These similarities drew attention to the issue of a formal account of the relationship between the two logics, which quickly became a subject of active research. Konolige [Kon88] proposed to translate a default into the autoepistemic formula: K :K: 1 : K: k : The translation was an attempt to re ect the intuition that in order to apply a default, its prerequisite must be derived and its justi cations must be consistent. To model the statement ....

....default logic or that the modal reading of a default proposed by Konolige is not appropriate. Thus, researchers began to look for other modal logics and for other translations. Konolige related default logic to a version of autoepistemic logic based on the notion of a strongly grounded expansion [Kon88]. Marek and Truszczy nski [MT89b] proposed an alternative translation and represented extensions as expansions of a modal nonmonotonic logic constructed by the method of McDermott from the weakest modal logic N . Truszczy nski [Tru91] found that the G odel translation of intuitionistic logic to ....

[Article contains additional citation context not shown here]

K. Konolige. On the relation between default and autoepistemic logic. Arti cial Intelligence, 35(3):343-382, 1988.

.... Take the AEL theory T obtained by replacing each UCL formula (63) with the AEL formula B : The translation in Proposition 15, while easy to justify directly, can also be obtained indirectly from Konolige s well known partial translation of default logic into autoepistemic logic [28], via Theorem 4. We can obtain a more general result of this kind by using a more complex translation, in which caused becomes, roughly speaking, truly believed. C C (64) where ; are nonmodal formulas. Take the AEL theory T obtained by replacing each UCL ....

Kurt Konolige. On the relation between default and autoepistemic logic. Arti cial Intelligence, 35:343-382, 1988.

....defect of Default Logic is, however, inability to reason by cases. A solution to this problem should enable reasoning by cases but may not result in introducing a contraposition for some of the default rules. Several proposals have been made to extend Default Logic with reasoning by cases [1, 4, 9, 13]. As Moinard shows [13] these approaches all introduce in one way or another some form of a contraposition. Moinard analyzes the problem, and presents a modified definition of a default extension that solves the problem. He also shows that a simple transformation of the default rules, makes it ....

....implication possesses a contraposition, so does a rule described by a (semi normal) free default rule. As we saw in the introduction this is not always desirable. When we wish to describe a rule that possesses no contraposition, a (seminormal) free default rule is not a good candidate. Konolige [9] proposes a slightly modified free default rule : fi to enable reasoning by cases. This default rule seems to enable reasoning by cases while avoiding the contraposition. The justification fi blocks the introduction of the material implication whenever it can be used in a contraposition. ....

K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343-382, 1988.

.... Furthermore, there is already a substantial body of results showing that autoepistemic logic offers a unified approach to several other modes of nonmonotonic reasoning (or at least substantial fragments of these) It has been shown that autoepistemic logic is closely related to default logic [61, 84], circumscription [63] McDermott and Doyle style nonmonotonic modal logics [135, 80] stable model semantics of logic programs [32] nonmonotonic truth maintenance systems [23] inheritance reasoning [35] and abduction [52] 1.2 Autoepistemic Logic Autoepistemic logic is a modal logic with an ....

....the initial assumptions correspond to the knowledge base of the system. We investigate a general setting where autoepistemic logic is defined on top of a given classical logic. Moore s [100] original formalization of autoepistemic logic is based on the classical propositional calculus. Konolige [61] shows how to extend the definition to the first order case where quantification into the scope of the belief operator is not allowed. We study autoepistemic reasoning in a more general setting where the underlying logic is not necessarily a first order calculus but could be, e.g. any modal ....

[Article contains additional citation context not shown here]

K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343--382, 1988.

....of statements or sentences which runs in that language will necessarily be sound and consistent relative to that logical formalism. One such language, implemented precisely to capture this feature of programs, is SDML [17] which corresponds to a fragment of strongly grounded auto epistemic logic [11]. Programming languages generally make it easier to do some things than others. Fortran is optimised for numerical calculation; LISP for functional programming, PROLOG for backwardchaining deduction, and so on. Numerical calculations, functional programming and backward chaining can all be ....

.... of cognition should be implemented as a software architecture (a sort of programming language but restricted to be sound and consistent with the theory and also restricted in its functionality so that it can only represent the specified cognitive relationships) The Soar software architecture [11] is an implementation of the Newell theory and it has been assessed against the performance of subjects in a large number of psychological experiments. Cooper, Fox, Farringdom and Shallice [5] showed that Soar is not the only possible implementation of the Newell theory. In addition, Ye and ....

Konolige, K. (1988), "On the relation between default and autoepistemic logic", Artificial Intelligence, v. 35, pp.343-382.

.... translations of reasoning tasks for the following modal nonmonotonic logics: Moore s autoepistemic logic [29] nonmonotonic logic N [26] also called iterative autoepistemic logic) reasoning with parsimoniously grounded expansions [13] and Konolige s system of moderately grounded expansions [24]. From a theoretical point of view, the feasibility of the current approach relies on the observation that the evaluation problem of quantified Boolean formulas, QSAT, is PSPACE complete, so any decision problem in PSPACE can be polynomially reduced to QSAT : In fact, the evaluation problem for ....

....Concerning the first expansion, the corresponding T full set is 1 = fLpg, since T [ fLpg j= p holds. The second expansion is characterised by the T full set f:Lpg, since we have that T [ f:Lpg 6j= p. Observe that SE T ( 2 ) does neither contain p nor :p. It has been argued in the literature [24, 26] that the first expansion is in some sense counterintuitive, since the assertion of p is based solely on the assumption that p is believed. The following subsections will deal with variations of autoepistemic logic which circumvent this problem. For an autoepistemic theory T having propositional ....

[Article contains additional citation context not shown here]

K. Konolige. On the Relation Between Default and Autoepistemic Logic. Artificial Intelligence, 35(3):343--382, 1988.

....set of statements or sentences which runs in that language will necessarily be sound and consistent relative to that logical formalism. One such language, implemented precisely to capture this feature of programs, is SDML [1] which corresponds to a fragment of strongly grounded autoepistemic logic [2]. Programming languages generally make it easier to do some things than others. Fortran is optimized for numerical calculation; LISP for functional programming, PROLOG for backward chaining deduction, and so on. Numerical calculations, functional programming and backward chaining can all be ....

Konolige, K. (1988), "On the relation between default and autoepistemic logic", Artificial Intelligence, v. 35, pp. 343-382.

....the model. Nonetheless, the model is consistent and sound relative to at least one logical formalism (and, though unproved, probably many such formalisms) The logical formalism under which the transition model is consistent and sound is a fragment of strongly grounded autoepistemic logic (FOSGAL)[8]. The proof of the consistency and soundness of the model relative to FOSGAL runs as follows: If a programming language corresponds to a logical formalism, then any program viewed as a set of statements or sentences which runs in that language will necessarily be sound and consistent relative to ....

Konolige, K. (1988), "On the relation between default and autoepistemic logic", Artificial Intelligence, v. 35, pp.343-382.

....expressive power if measured by the levels of PH. The expressibility issue can also addressed in terms of translation functions between theories of non monotonic logics. For instance, a variety of translation functions have been proposed to transform a default theory into an autoepistemic one [2, 9, 12, 13, 17, 25, 27] and back [11, 18] such that sets of conclusions are preserved to a reasonable degree in the translation. Also, translation functions between various kinds of default theories have been considered [2, 6, 15] In fact, complexity results are based on polynomial transformations between decision ....

....the propositional parts of expansions and extensions in question coincide. 2 A number of principles have been proposed to translate default theories into autoepistemic ones. Basically, the problem is to translate a default ff : fi 1 ; fi n =fl into an autoepistemic sentence. Konolige [13] introduces a translation Bff :B:fi 1 : B:fin fl for a default. Unfortunately, the resulting translation function TrK for default theories is not faithful in general, as shown by Marek and Truszczy#ski [17] As a response to this problem, they handle justications fi i dioeerently: B:fi ....

[Article contains additional citation context not shown here]

K. Konolige. On the relation between default and autoepistemic logic. Articial Intelligence, 35:343382, 1988.

....19 person exists, or by carefully sifting all the available evidence, but simply because if he had an elder brother he would know about him. In its original form autoepistemic logic is a purely propositional modal logic, with no means of incorporating quanti ers or individual variables. Konolige [73, 72] extends Moore s approach to a rst order system initially [73] to a a system that does not allow quantifying in to the scope of a modality and later [72] to a full rst order system. 4.2 Imprecise information The pioneering work in combining fuzzy sets and logic to allow the representation of ....

....but simply because if he had an elder brother he would know about him. In its original form autoepistemic logic is a purely propositional modal logic, with no means of incorporating quanti ers or individual variables. Konolige [73, 72] extends Moore s approach to a rst order system initially [73] to a a system that does not allow quantifying in to the scope of a modality and later [72] to a full rst order system. 4.2 Imprecise information The pioneering work in combining fuzzy sets and logic to allow the representation of and inference with vague information was performed by Zadeh ....

Konolige, K. (1988) On the relation between default and autoepistemic logic, Articial Intelligence, 35, 343-382.

....semantics and resulted in a uniform semantic framework for default logic, surprisingly similar to that discovered in the case of autoepistemic logic. In fact, in (Denecker et al. 1999) we proved that both frameworks are isomorphic and we argued that under the translation proposed in (Konolige, 1988), default logic can be viewed as a fragment of autoepistemic logic. In this paper we extract essential algebraic elements underlying unified semantic frameworks for logic programming, autoepistemic logic and default logic developed in (Fitting, 1999; Denecker et al. 1998; Denecker et al. 1999) ....

....W and the restriction of the operator E Delta(P ) to this sublattice essentially coincides with T P . It follows that 16 all the derived operators are similarly related, and we obtain a perfect match between the semantics for logic programming and the semantics for default logic. Similarly, in (Konolige, 1988) it was proposed to interpret a default fi 1 : fi m : fl 1 ; fl n ff as a modal formula Kfi 1 : Kfi m :K:fl 1 : K:fl n oe ff: It turns out that under this translations the operators E Delta and D T ( Delta) coincide (here T ( Delta) is the modal image of a ....

Konolige, K. (1988). On the relation between default and autoepistemic logic.

....logic was proposed by Moore [Moo84] to describe the belief states of rational agents reflecting upon their own beliefs and disbeliefs. Although the motivation and syntax of both logics are different, it has been clear for a long time that they are closely related. However, despite much work [Kon88, MT89a, Tru91, MT93, Got95] no truly satisfactory account of the relationship was found. Konolige [Kon88] related default logic to a version of autoepistemic logic based on the notion of a strongly grounded expansion a concept that depends on a syntactic representation of a theory. Marek and Truszczynski related default ....

....their own beliefs and disbeliefs. Although the motivation and syntax of both logics are different, it has been clear for a long time that they are closely related. However, despite much work [Kon88, MT89a, Tru91, MT93, Got95] no truly satisfactory account of the relationship was found. Konolige [Kon88] related default logic to a version of autoepistemic logic based on the notion of a strongly grounded expansion a concept that depends on a syntactic representation of a theory. Marek and Truszczynski related default logic to two modal nonmonotonic logics related but different from ....

[Article contains additional citation context not shown here]

K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35(3):343--382, 1988.

....of W and the restriction of the operator E (P ) to this sublattice essentially coincides with T P . It follows that all the derived operators are similarly related, and we obtain a perfect match between the semantics for logic programming and the semantics for default logic. Similarly, in (Konolige, 1988) it was proposed to interpret a default 1 : m : 1 ; n as a modal formula K 1 : K m :K: 1 : K: n : It turns out that under this translations the operators E and D T( coincide (here T( is the modal image of a default theory under ....

Konolige, K. (1988). On the relation between default and autoepistemic logic. Articial Intelligence, 35(3):343-382.

No context found.

Konolige, K. 1987. On the relation between default and autoepistemic logic. In Readings in Nonmonotonic Reasoning, M. L. Ginsberg, Ed. Kaufmann, Los Altos, CA, 195-226.

No context found.

K. Konolige, `On the relation between default and autoepistemic logic', in Arti cial Intelligence, 35, pp. 343-382, 1989.

No context found.

K. Konolige. On the relation between default and autoepistemic logic. Arti cial Intelligence, 35:343-382, 1988.

No context found.

Kurt Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343--382, 1988.

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Konolige K., On the relation between default and autoepistemic logic, Articial Intelligence, 35:343382, 1988.

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K. Konolige. On the relation between default and autoepistemic logic. Arti cial Intelligence Journal, 35(3):343-382, 1988.

No context found.

K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence Journal, 35:343--382, 1988.

No context found.

K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence Journal, 35(3):343--382, 1988.

No context found.

K. Konolige. On the relation between default and autoepistemic logic. In M. L. Ginsberg, editor, Readings in Non-Monotonic Reasoning, pages 195--226. Morgan Kaufmann Publishers, Inc., 1987.

No context found.

K. Konolige. On the relation between default and autoepistemic logic. Articial Intelligence, 35:343-382, 1988.

No context found.

K. Konolige. On the relation between default and autoepistemic logic. Articial Intelligence, 35:343382, 1988.

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