V. W. Marek and M. Truszczynski. Modal logic for default reasoning. In Annals of Mathematics and Artificial Intelligence, pages 275--302, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....grounded versions of autoepistemic reasoning were developed with the aim of establishing a correspondence between autoepistemic reasoning and reasoning in Reiter s default logic. Konolige [61, 62] proposes the classes of moderately grounded and strongly grounded expansions. Marek and Truszczy nski [84, 85, 86] continue the work and introduce several classes of expansions: iterative, strongly iterative, and robust expansions. Shvarts [135] and Marek et al. 80] indicate that some weakly grounded expansions can be eliminated by considering appropriate McDermott and Doyle style nonmonotonic modal logics. ....

....between autoepistemic logic and default logic. This translation is studied further by Marek and Truszczy nski [84, 89] Several other embeddings of default logic into variants of autoepistemic logic, McDermott and Doyle style nonmonotonic modal logics and other modal systems have been studied [41, 56, 75, 77, 78, 85, 86, 108, 111, 145, 144]. Konolige [63] shows how to capture circumscription in autoepistemic logic. The connections between different semantics of logic programs and autoepistemic logic have been investigated intensively [10, 23, 29, 32, 55, 81, 82, 116, 118, 117] Autoepistemic logic is shown to provide a logical basis ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy'nski. Modal logic for default reasoning. In Preprints of the 3rd International Workshop on Nonmonotonic Reasoning, pages 247--258, South Lake Tahoe, California, May 1990.

....nonmonotonic objects were de ned using a similar xed point construction. This and subsequent paper [23] gave rise to a study of autoepistemic logic [24] and of a whole range of modal nonmonotonic logics based on negative introspection in the works of Marek, Truszczy nski and Schwarz (see, e.g. [17, 18, 16, 21, 27, 30]) Despite the di erence in the underlying language, the similarity between the above two approaches to nonmonotonic reasoning were noticed early, and a number of attempts has been made to clarify their relationship. Thus, Konolige [13] attempted to translate default logic into Moore s ....

....but otherwise will involve the same rules as general default consequence relations. Modal default consequence relations will turn out to be an especially suitable tool for studying modal nonmonotonic reasoning. Thus, both autoepistemic reasoning ( 24] and reasoning with negative introspection ([23, 18, 16]) will acquire a natural characterization in this framework. As has been shown in [2] under certain reasonable conditions modal consequence relations are reducible to the associated nonmodal default consequence relations in a way that preserves the associated nonmonotonic objects. These results ....

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W. Marek and M. Truszczynski (1990). Modal logic for default reasoning. Annals of Mathematics and Articial Intelligence 1:275-302.

....situation by facts (28) while the goal situation is specified by query (29) This query enforces that only those answer sets are computed, in which the conjunction of the query literals is true. 5 Computational Complexity As for the classical nonmonotonic formalisms (Marek Truszczynski, 1991; Marek Truszczynski, 1990; Reiter, 1980) two important decision problems, corresponding to two different reasoning tasks, arise in DLP : Brave Reasoning) Given a DLP program P and a ground literal L, decide whether there 5 We use constraints for clarity, but they can be eliminated by rewriting B: to p B; not p: ....

Marek, W., & Truszczynski, M. (1990). Modal Logic for Default Reasoning. Annals of mathematics and artificial intelligence, 1(1-4), 275--302.

....between autoepistemic logic and default logic. This translation is studied further by Marek and Truszczy#ski [70, 75] Several other embeddings of default logic into variants of autoepistemic logic, McDermott and Doyle style nonmonotonic modal logics and other modal systems have been studied [38, 47, 63, 64, 65, 72, 71, 88, 90, 112, 113, 119, 118]. Konolige [52] shows how to capture circumscription in autoepistemic logic. The connections between different semantics of logic programs and autoepistemic logic have been investigated intensively [12, 22, 29, 31, 46, 68, 69, 96, 99, 98] Autoepistemic logic is shown to provide a logical basis ....

W. Marek and M. Truszczy#ski. Modal logic for default reasoning. In Preprints of the 3rd International Workshop on Nonmonotonic Reasoning, pages 247258, South Lake Tahoe, California, May 1990.

....and autoepistemic logic are capable of carrying out very similar inferences. However, we have preferred autoepistemic logic for the sake of its uniform syntax for knowledge representation (autoepistemic formulae like the one above) In default logic, defaults form a separate syntactic category. Marek and Truszczy#ski [ 1990a; 1991 ] further introduce a variant of autoepistemic logic, the nonmonotonic modal logic N , designed for default reasoning. The stable model semantics of logic programs is in close relationship with autoepistemic reasoning [ Gelfond and Lifschitz, 1988 ] In fact, the various semantics of ....

....L Delta in Equation (2) McDermott and Doyle [ 1980; 1982 ] have proposed a scheme for nonmonotonic modal logics where a modal logic S is used for positive introspection: Delta = Cn S ( Sigma [ L Delta) Marek, Shvarts and Truszczy#ski [ 1991 ] have studied these logics in greater depth. Marek and Truszczy#ski [ 1990b ] use the modal logic of necessitation N for realizing the positive introspection capability of the agent. The modal logic of necessitation is a nonstandard modal logic. It is simply classical propositional calculus equipped with the necessitation rule iOE LOEj of standard modal logics. We let ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy#ski. Modal logic for default reasoning. In Preprints of the 3rd International Workshop on Nonmonotonic Reasoning, pages 247258, South Lake Tahoe, California, May 1990.

....[7] all the further studies focused, in fact, on the connection between Moore s notion of groundedness in autoepistemic logic and suitable variations on the modal representation of default logic. The breakthrough in the modal study of default logic came from Marek, Shwartz and Truszczynski in [19, 10, 24, 11, 12, 9, 20] who reconsider the earliest attempt of McDermott and Doyle and of McDermott. In fact, in McDermott and Doyle s fix point equation it is sufficient to strengthen classical logic with the necessitation rule, that is the logic N , which however has been done by McDermott who devised the needs of ....

V. W. Marek and M. Truszczynski. Modal logic for default reasoning. In Annals of Mathematics and Artificial Intelligence, pages 275--302, 1990.

....ability is definitely disregarded. Therefore, we cannot consider the above equation (3) as a commonsense statement, although it has many advantages like, for example, providing an embedding for default reasoning in a wide class of modal logics (see (McDermott and Doyle, 1980; McDermott, 1982; Marek and Truszczynski, 1990; Marek and Truszczynski, 1993; Marek et al. 1993; Schwarz and Truszczynski, 1994; Schwarz, 1995) Let us reformulate the strict relation between definability and self reference. As we have argued, classical definability is too strong because it is functional, i.e. it commits to uniqueness, and ....

.... in an unpublished manuscript of 1980, appeared later in (Stalnaker, 1993) with the introduction of the notion of stable set, and afterwards expanded by Moore in (Moore, 1985) The connection with default logic has been proposed by the work of Konolige (Konolige, 1988) and further developed in (Marek and Truszczynski, 1990). Marek and Truszczynski (Truszczynski, 1991; Marek and Truszczynski, 1993; Marek et al. 1993) have shown that with the negation as failure to prove paradigm a family of modal logics can be devised to capture default reasoning. In fact, expansions with in this family of modal logics are stable ....

Marek, V. W. and Truszczynski, M. (1990). Modal logic for default reasoning. In Annals of Mathematics and Artificial Intelligence, pages 275--302.

....all the further studies focused on the connection between Moore s notion of groundedness in autoepistemic logic and suitable variations on the modal representation of Default logic. The breakthrough in the modal study of Default logic comes from Marek, Schwartz and Truszczynski in (Schwarz, 1990; Marek and Truszczynski, 1990; Truszczynski, 1991; Marek and Truszczynski, 1992; Marek and Truszczynski, 1993; Marek et al. 1993; Schwarz and Truszczynski, 1994) who reconsider the earliest attempt of McDermott and Doyle and of McDermott. In fact in the McDermott and Doyle s fixed point equation it is sufficient to ....

....KD4Z. C L is a Reiter extension iff CnKD4Z (2C) j CnKD4Z (I [ f:2fl : fl 62 Cg) The above characterization is in the same style of the negation by failure paradigm, the only difference relies in the default s translation, which (see (Amati et al. 1996) would not suits for the logic devised by (Marek and Truszczynski, 1990)) We have given an even more sophisticated characterization, as the ongoing discussion shall show. In (Amati et al. 1994) we have proved that fixed points are definable in KD4Z. In other words, given a sentence E, in which a propositional variable p occurs, there are sentences C, not containing ....

Marek, V. W. and Truszczynski, M. (1990). Modal logic for default reasoning. In Annals of Mathematics and Artificial Intelligence, pages 275--302.

....arises from incomplete information. The retracted conclusions are usually those made under incomplete information. Many nonmonotonic formalisms have been proposed to cope with the problem of reasoning under incomplete information. The most well known include modal nonmonotonic logics [15, 14, 9], autoepistemic logic[16, 10] default logic Research supported by the National Science Council under Grant NSC84 2213 E 002019. and its variants[20, 3, 11] circumscription[12, 13] and closed world assumptions (CWA) 19] One common feature of these formalisms is that their semantics all ....

W. Marek and M. Truszczy'nski. "Modal logic for default reasoning". Annals of Mathematics and Artificial Intelligence, 1:275--302, 1990.

....[7] all the further studies focused, in fact, on the connection between Moore s notion of groundedness in autoepistemic logic and suitable variations on the modal representation of default logic. The breakthrough in the modal study of default logic came from Marek, Shwartz and Truszczy nski in [19, 10, 24, 11, 12, 9, 20] who reconsider the earliest attempt of McDermott and Doyle and of McDermott. In fact, in McDermott and Doyle s fix point equation it is sufficient to strengthen classical logic with the necessitation rule, that is the logic N , which however has been done by McDermott who devised the needs of ....

V. W. Marek and M. Truszczy'nski. Modal logic for default reasoning. In Annals of Mathematics and Artificial Intelligence, pages 275--302, 1990.

....base and queries are both epistemic formulae while the underlying logic is nonmonotonic. 4 Appendix In this section we will briefly discuss the relationship between epistemic specifications and some other general purpose nonmonotonic formalisms such as autoepistemic logics [MD80] Moo85] [MT90], and default logic of R. Reiter [Rei80] and its extension [GLPT91] By now we have a reasonably good understanding of the relationship between these formalisms and special classes of epistemic specifications. For the equivalence results about various subclasses see for instance [Gel87] BF87] ....

Wiktor Marek and Miroslaw Truszczy'nski. Modal logic for default reasoning. To appear, 1990.

....default logic [14] and Moore s autoepistemic logic [10] into reconsideration. In light of earlier research results, default reasoning is often seen as a special case of autoepistemic reasoning. This view is supported, e.g. by the results of Gottlob [3] Konolige [4, 5, 6] Marek and Truszczy#ski [8, 9], Niemel# [12] and Truszczy#ski [15] To the contrary, we demonstrate how autoepistemic reasoning can be seen as a form of default reasoning. This seemingly straightforward result has important consequences as it (i) indicates that autoepistemic logic and default logic are of equal generality, ....

....reasoning, but in a rather non trivial way. A reasonable correspondence follows by composing translations provided by Truszczy#ski [15] and Gottlob [3] This involves an intermediary representation of a default theory as a theory in strong autoepistemic logic proposed by Marek and Truszczy#ski [8]. Strong autoepistemic logic is a variant that considers only the iterative expansions of an autoepistemic theory that form a subclass of its stable expansions. This paper proceeds in the opposite direction starting from a characterization of stable expansions due to Marek, Schwarz and ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy#ski, `Modal logic for default reasoning', Annals of Mathematics and Artiøcial Intelligence, 1, 275302, (1990).

....grounded versions of autoepistemic reasoning were developed with the aim of establishing a correspondence between autoepistemic reasoning and reasoning in Reiter s default logic. Konolige [61, 62] proposes the classes of moderately grounded and strongly grounded expansions. Marek and Truszczy nski [84, 85, 86] continue the work and introduce several classes of expansions: iterative, strongly iterative, and robust expansions. Shvarts [135] and Marek et al. 80] indicate that some weakly grounded expansions can be eliminated by considering appropriate McDermott and Doyle style nonmonotonic modal logics. ....

....between autoepistemic logic and default logic. This translation is studied further by Marek and Truszczy nski [84, 89] Several other embeddings of default logic into variants of autoepistemic logic, McDermott and Doyle style nonmonotonic modal logics and other modal systems have been studied [41, 56, 75, 77, 78, 85, 86, 108, 111, 145, 144]. Konolige [63] shows how to capture circumscription in autoepistemic logic. The connections between different semantics of logic programs and autoepistemic logic have been investigated intensively [10, 23, 29, 32, 55, 81, 82, 116, 118, 117] Autoepistemic logic is shown to provide a logical basis ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy'nski. Modal logic for default reasoning. In Preprints of the 3rd International Workshop on Nonmonotonic Reasoning, pages 247--258, South Lake Tahoe, California, May 1990.

....knowledge base of default rules with one containing autoepistemic formulas. Most of the efforts in relating the two logics focus on the syntactic manipulation of default rules to embed default logic into autoepistemic logic using some particular translation schema and modal system [Konolige, 1988; Marek and Truszczy nski, 1990; Truszczy nski, 1991b; Truszczy nski, 1991a] However, most of these efforts impose additional constraints on autoepistemic logic, such as requiring stronger groundedness or using different base modal systems. Thus, although default logic can be translated into some variants of autoepistemic ....

....not correspond to default extensions. For example, Konolige [Konolige, 1988; Konolige, 1989] required extra groundedness conditions to select the appropriate stable expansions. These strongly grounded expansions are sensitive to the syntactic representation of the formulas. Marek and Truszczy nski [Marek and Truszczy nski, 1990; Truszczy nski, 1991b; Truszczy nski, 1991a] showed that default logic can be translated using various schemes into modal systems ranging from N (modal system with the rule of necessitation but no axioms) to S4F [Segerberg, 1971] S4 with F: OE :L:L L( L:OE ) Notably, however, the ....

[Article contains additional citation context not shown here]

Wiktor Marek and Miros/law Truszczy'nski, "Modal Logic for Default Reasoning," Annals of Mathematics and Artificial Intelligence, 1:275--302, 1990.

....between autoepistemic logic and default logic. This translation is studied further by Marek and Truszczy nski [70, 75] Several other embeddings of default logic into variants of autoepistemic logic, McDermott and Doyle style nonmonotonic modal logics and other modal systems have been studied [38, 47, 63, 64, 65, 72, 71, 88, 90, 112, 113, 119, 118]. Konolige [52] shows how to capture circumscription in autoepistemic logic. The connections between different semantics of logic programs and autoepistemic logic have been investigated intensively [12, 22, 29, 31, 46, 68, 69, 96, 99, 98] Autoepistemic logic is shown to provide a logical basis ....

W. Marek and M. Truszczy'nski. Modal logic for default reasoning. In Preprints of the 3rd International Workshop on Nonmonotonic Reasoning, pages 247--258, South Lake Tahoe, California, May 1990.

....extensions that have no counterparts in default logic. The first attempt [Konolige, 1988] was unsuccessful, and this has led to the invention of supergrounded and robust extensions (see ( Marek and Truszczy nski, 1989] Sections 2. 3 and 3) Further work in this direction is described in [Marek and Truszczy nski, 1990]. The available reductions of defaults to epistemic formulas are not completely satisfactory. What makes the situation even more complicated is the fact that autoepistemic logic is merely one point in the whole spectrum of nonmonotonic modal systems introduced in [McDermott, 1982] and possibly ....

Wiktor Marek and Miros/law Truszczy'nski. Modal logic for default reasoning. To appear, 1990.

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V. W. Marek and M. Truszczynski. Modal logic for default reasoning. In Annals of Mathematics and Artificial Intelligence, pages 275--302, 1990.

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