Viktor M. Marek and Mirek Truszczynski. Nonmonotonic Logics; Context-Dependent Reasoning. Springer Verlag, Berlin-Heidelberg-New York, 1st edition, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....facts, together with the default rules, gives rise to a number of extensions (which can be considered belief sets) An operator that assigns the corresponding set of extensions to each set of initial facts is a belief set operator. The kernel of this operator yields the sceptical (see e.g. [11]) conclusions. Often, as is the case in the application, after a number of belief sets have been generated, the process will focus on (or make a commitment to) one (or possibly more) of the belief sets, because it seems the most promising, or interesting, possible view on the world. This ....

V.W. Marek and M. Truszczynski, Nonmonotonic logics; context-dependent reasoning, Springer-Verlag, 1993.

....facts, together with the default rules, gives rise to a number of extensions (which can be considered belief sets) An operator that assigns the corresponding set of extensions to each set of initial facts is a belief set operator. The kernel of this operator yields the sceptical (see e.g. [11]) conclusions. Often, as is the case in the application, after a number of belief sets have been generated, the process will focus on (or make a commitment to) one (or possibly more) of the belief sets, because it seems the most promising, or interesting, possible view on the world. This ....

....6.2. The Logical Techniques Used The idea that information about the world can often be interpreted in different and conflicting manners was a central theme in the research reported in [14] 8] Using techniques to formalise non monotonic reasoning, such as default logic (e.g. 13] 5] [11]) often different (and often conflicting) possible outcomes of a reasoning process are obtained. In the area of research on non monotonic reasoning, in general this is considered to be disturbing (e.g. it is called the multiple extension problem) To come to one set of conclusions, in the ....

V.W. Marek and M. Truszczynski, Nonmonotonic logics; context-dependent reasoning, Springer-Verlag, 1993.

....together with the default rules, gives rise to a number of extensions (which can be considered belief sets) An operator that assigns the corresponding set of extensions to each set of initial facts is a multi interpretation operator. The kernel of this operator yields the sceptical (see e.g. [10]) conclusions. Often, after a number of belief sets have been generated, the reasoning agent will focus on (or make a commitment to) one (or possibly more) of the belief sets, because it seems the most promising, or interesting, possible view on the world. This selection process can be ....

V.W. Marek and M. Truszczynski, Nonmonotonic logics; context-dependent reasoning, Springer-Verlag, 1993.

....by a person, who is usually a specialist, will be abstracted, and stored into the case repository. 3. l JECA Rules We have extended the well known ECA rules specification as Justified Event Condition Action (JECA) rules to model business logic based on work in context dependent reasoning [7]. There are several workflow prototypes (e.g. 8, 9] that have adopted ECA rules as modeling tools. However, the contexts that can be captured by ECA rules are limited. The C in an ECA rule, which is used to capture rules evaluation context, is used as a condition that should be satisfied so that ....

....a justification for that JECA rule. If the justification cannot be evaluated true, then the JECA rule will not be disqualified. So the action in that JECA rule can be executed if the risk factor of heart murmur is true. 2 JECA rules evaluation To apply the context dependent reasoning processes [7], those JECA rules are transformed into a form that is usually used in the context dependent reasoning, called default [7] A default has three parts, prerequisite (P) justification (J) and consequence (C) specified in logic expressions. Those defaults are constructed through JECA rules with ....

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V. Marek, M. Truszczynski, Non-monotonic Logic, Context-Dependent Reasoning, Springer-Verlag, 1993

.... and has attractive complexity (quadratic in the number of atoms) STABLE can become inconsistent (programs may have no stable models) answering queries can not be restricted to the call graph below that query, and the complexity of STABLE lies one level higher in the polynomial hierarchy (see [61, 54, 62]) Another difference of STABLE and WFS is that for a given program there might be several stable models. Each stable model represents a particular consistent view of the world, while the union of any two is inconsistent. This is much like the extensions in default logic [71] and this viewpoint is ....

Wiktor Marek and Mirek Truszczy nski. Nonmonotonic Logics; Context-Dependent Reasoning. Springer, Berlin, 1st edition, 1993.

....results. For instance, the analysis of the frame problem leads to the acceptance of minimal models as the class of desired models and, subsequently to the notion of circumscription ( McC80] The analysis of closed systems of beliefs leads to the acceptance of supported models of programs ([Cla78, MT93]) In this paper we are looking at logical theories (described by means of a disjunctive program, possibly with negation in the body) as expressing a possible causal relationship between various atoms of the underlying language. Moreover we want to express the interpretation of negation as ....

....C = p q 1 ; q n ; s 1 ; sm (p; q 1 ; q n ; s 1 ; s m are atoms) from P : rk(p) rk(q i ) i n , and rk(p) rk(s j ) j m . Let P be a stratified normal logic program. We can assign to P a model M supp P , called the perfect model ( ABW88] as presented in [MT93]) as follows: first, split the program P into the union of programs P i according to the ranks of heads. Let P = S n2IN P n be this decomposition. Define M 0 to be the least model of P 0 (notice that according to stratification condition, P 0 , if non empty, must be a Horn program) Next, ....

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V.W. Marek and M. Truszczy nski. Nonmonotonic Logics; Context-Dependent Reasoning. Springer, Berlin, 1st edition, 1993.

....all i = 0; 1; E i 1 = Cn(E i ) apply D;E (E i ) 5) Then E is an extension of (D; W ) if and only if E = 1 [ i=0 E i : 6) Default logic is one of the most prominent formalizations of nonmonotonic reasoning. The books of Besnard [7] Etherington [25] and Marek and Truszczy#ski [76] are good sources on default logic. There is a body of results indicating that default logic can capture a large number of dioeerent forms of nonmonotonic reasoning. Default logic is especially closely related to reasoning in logic programs and deductive databases [10, 11, 32] Default logic has ....

....only if Delta = fOE j Sigma [ L Delta S OEg (7) where S is the derivability relation of the logic S. The work of McDermott and Doyle [82, 81] was extented rst by Shvarts [108] and then by Marek et al. 67] A good source on nonmonotonic modal logics is the book of Marek and Truszczy#ski [76]. Statements of the type ibirds typically AEyj can be formalized in nonmonotonic modal logics using the formula b :L:f f: If the operator L is read iis believedj, the formula states that if a bird is not believed not to AEy, it AEies. Autoepistemic logic was introduced by Moore [84] as a ....

W. Marek and M. Truszczy#ski. Nonmonotonic Logic, Context-Dependent Reasoning. Springer-Verlag, Berlin, 1993.

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V. W. Marek and M. Truszczynski, Nonmonotonic Logic. Context-Dependent Reasoning, Springer-Verlag, 1993.

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V. W. Marek and M. Truszczynski, Nonmonotonic Logic. Context-Dependent Reasoning, Springer-Verlag, 1993.

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V. Marek and M. Truszczynski, Nonmonotonic Logic, Context-Dependent Reasoning, Springer-Verlag, 1993.

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V.W. Marek & M. Truszczynski, Nonmonotonic Logic, Context-Dependent Reasoning, Springer-Verlag, Berlin, 1993.

.... semantics (propositional circumscription) McC80,Lif88] logic programming with stable model semantics [GL88] and disjunctive logic programming with the answer set semantics [GL91] are among most commonly studied and broadly used knowledge representation formalisms (we refer the reader to [MT93,BDK97] for a detailed treatment of these logics and additional pointers to literature) Recently, they have been receiving much attention due to their applications in answer set programming (ASP) an emerging declarative programming paradigm. To solve a problem in ASP, programmers write a logic ....

.... each disjunctive program clause c 1 : c p a 1 ; a r ; not(b 1 ) not(b s ) in P with a CNF clause :a 1 : a r b 1 : b s c 1 : c p : It is well known that stable models (answer sets) of (disjunctive) logic program P are minimal models of T (P ) [MT93]. Let us assume that test stb(P; M) and test anset(P; M) are algorithms to check whether a set of atoms M is a stable model and an answer set, respectively, of a program P . To compute stable models of a logic program P that are consistent with a set of literals L, we first compute the CNF ....

W. Marek and M. Truszczy'nski. Nonmonotonic Logic; Context-Dependent Reasoning. Springer-Verlag, Berlin, 1993.

....and precise account of the relationship between the two logics in question. The default logic introduced by Reiter [Rei80] and the autoepistemic logic introduced by Moore [Moo84, Moo85] are among the most widely studied nonmonotonic knowledge representation systems. Research monographs [Bes89, MT93, Ant97] provide extensive presentations of these two logics, and of their properties. The default and the autoepistemic logics were designed to model commonsense forms of reasoning, in particular, reasoning patterns of the form in the absence of any information to the contrary infer . Such patterns ....

....D T . Its fixpoints, and fixpoints of the operators that can be derived from D T , determine all major semantics for autoepistemic logic. We will now develop a similar treatment of default logic. We start by recalling basic concepts in default logic. For more details we refer the reader to [MT93]. A default is an expression of the form ; where ff, fi 1 ; fi k and fl are propositional formulas from the language L. The formula ff is called the prerequisite of the default. The formulas fi 1 ; fi k are called its justifications. Finally, the formula fl is called the ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy'nski. Nonmonotonic Logic; Context-Dependent Reasoning. Springer-Verlag, 1993.

....and precise account of the relationship between the two logics in question. The default logic introduced by Reiter [Rei80] and the autoepistemic logic introduced by Moore [Moo84, Moo85] are among the most widely studied nonmonotonic knowledge representation systems. Research monographs [Bes89, MT93, Ant97] provide extensive presentations of these two logics, and of their properties. The default and the autoepistemic logics were designed to model commonsense forms of reasoning, in particular, reasoning patterns of the form in the absence of any information to the contrary infer . Such patterns ....

....operator D T . Its xpoints, and xpoints of the operators that can be derived from D T , determine all major semantics for autoepistemic logic. We will now develop a similar treatment of default logic. We start by recalling basic concepts in default logic. For more details we refer the reader to [MT93]. A default is an expression of the form ; where , 1 ; k and are propositional formulas from the language L. The formula is called the prerequisite of the default. The formulas 1 ; k are called its justi cations. Finally, the formula is called the consequent of ....

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W. Marek and M. Truszczynski. Nonmonotonic Logic; Context-Dependent Reasoning. Springer-Verlag, 1993.

....In particular, norms can conflict in reality In formal terms: O.1 is not equivalent with .12 (But, of course, in practice, when we encounter conflicting duties, we must try and resolve these. This is very much related to defeasible (nonmonotonic) reasoning in AI research (cf. e.g. Luk90] [MT93] as excellent introductions to the area of nonmonotonic reasoning; in [LHM95] the emphasis is on the dynamics of default reasoning viewed from the stand point of a reasoning agent. However, the dynamics of reasoning is also studied in a more general context of complex reasoning patterns like in ....

V.W. Marek & M. Truszczynski, Nonmonotonic Logic, Context-Dependent Reasoning, Springer-Verlag, Berlin, 1993.

....(stronger) definition of permission together with admissible contexts for actions, but also here dynamic logic is a crucial ingredient of the approach. 3. In AI research, dynamics comes in when considering complex reasoning patterns, such as defeasible (nonmonotonic) reasoning (cf. e.g. Luk90] [MT93] as excellent introductions to the area of nonmonotonic reasoning; in [LHM94] the emphasis is on the dynamics of default reasoning viewed from the stand point of a reasoning agent. However, the dynamics of reasoning is also studied in a more general context of complex reasoning patterns like in ....

V.W. Marek & M. Truszczynski, Nonmonotonic Logic, Context-Dependent Reasoning, Springer-Verlag, Berlin, 1993.

....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 ....

.... Another problem is related to the fixpoint definitions of extensions (in the case of default logic) and expansions (in the case of autoepistemic logic) They 1 For a detailed discussion of these two formalisms and of their applications, and for additional references, the reader is referred to [MT93]. provide no insights into constructive processes agents might use to build their belief sets based on default or modal theories describing base facts. Finally, there is a problem of high computational complexity of reasoning with extensions and expansions. The problems to decide the existence of ....

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W. Marek and M. Truszczy'nski. Nonmonotonic logics; context-dependent reasoning. Springer-Verlag, Berlin, 1993.

....belief set (although new belief sets may become possible at this point) This new evidence can come as new facts already present in the belief set, and as new rules that are satisfied by the belief set. The first of these possibilities was studied in the case of default logic and logic programming [Rei80, MT93a]. The second one has not been explicitly studied in the literature so far. We will now prove two versions of confirmation of evidence property for revision programming. In the next result, the assumption R Xi B R Xi I means that B is closer to R than I. That is, it contains additional ....

....to show that a revision program is coherent if and only if P has a three valued model. We conclude this section by introducing another semantics for revision programs the semantics of supported revisions. It is based on similar ideas as the semantics of supported models for logic programs [Cla78, MT93a]. 18 Definition 3.11 A set of atoms R is a P supported revision of I if head(P R ) is coherent and R = I Phi head(P R ) We will now present several properties of supported revisions. Our results generalize two well known results on logic programming: 1) each supported model of a logic ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy'nski. Nonmonotonic logics; context-dependent reasoning. Berlin: Springer-Verlag, 1993.

....results. For instance, the analysis of the frame problem leads to the acceptance of minimal models as the class of desired models and, subsequently to the notion of circumscription ( McC80] The analysis of closed systems of beliefs leads to the acceptance of supported models of programs ([Cla78, MT93]) In this paper we are looking at logical theories (described by means of a disjunctive program, possibly with negation in the body) as expressing a possible causal relationship between various atoms of the underlying language. Moreover we want to express the interpretation of negation as ....

....every rule C = p q 1 ; q n ; s 1 ; sm (p; q 1 ; q n ; s 1 ; s m are atoms) from P : rk(p) rk(q i ) i n, and rk(p) rk(s j ) j m. Let P be a stratified normal logic program. We can assign to P a model, called the perfect model ( ABW88] as presented in [MT93]) as follows: first, split the program P into the union of programs P i according to the ranks of heads. Let P = S n2IN P n be this decomposition. Define M 0 to be the least model of P 0 (notice that according to stratification condition, P 0 , if non empty, must be a Horn program) Next, ....

Wiktor Marek and Mirek Truszczy'nski. Nonmonotonic Logics; Context-Dependent Reasoning. Springer, Berlin, 1st edition, 1993.

....defaults. 1 Introduction Default logic, introduced by Reiter [ 1980 ] is one of the most extensively studied nonmonotonic systems. Several recent research monographs offer a comprehensive presentation of theoretical and practical aspects of default logic [ Besnard, 1989; Brewka, 1991b; Marek and Truszczy nski, 1993 ] Default logic was designed to handle reasoning from incomplete information. It allows us to draw conclusions on the basis of the lack of evidence to the contrary . This formalism assigns to a default theory a collection of theories called extensions. They describe possible belief sets of an ....

....property of semi monotonicity of constrained default logic. It exploits the fact that constrained extensions can be produced by processing defaults according to any well ordering. This is very similar to the corresponding property of normal default theories in the logic of Reiter (Theorem 4. 3, Marek and Truszczy nski, 1993 ] In fact, our characterization of constrained default logic provides an alternative argument that for normal default theories constrained and standard default logics coincide. We assume that the set of the atoms of our language L is denumerable. Consequently, the set of all defaults over the ....

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W. Marek and M. Truszczy 'nski. Nonmonotonic logics; context-dependent reasoning. Berlin: Springer-Verlag, 1993.

....of i C is a prime clause of . b) for all positive databases D 1 = U; 1 ) 1 is logically equivalent to i = 1 (up to the ordering of clauses and disjuncts) 2. 3 Default logic Default logic [34] is one of the best known formalizations of nonmonotonic reasoning (see [27, 29] for extensive studies of the subject) A default (x) is a rule of the form (x) 1 (x) n (x) x) also written ( x) 1 (x) n (x) x) such that (x) 1 (x) n (x) x) are rst order formulas whose free variables are among those of x = x 1 ; ....

....theory T = hW; i. Then, E = Th(W [ CONS(GD( E) The converse is not true in general. However, from the above quasi inductive characterization of extensions, one can easily obtain the following result, in the spirit of Marek and Truszczy nski s characterizations based on well orderings (cf. [29]) Lemma 2.4 Let T = hW; i be a nite closed default theory and let E be a set of sentences. Then, E is an extension of T i (a) E = Th(W [ CONS(GD( E) and (b) there exists a strict partial order 8 on GD( E) such that for every = 1 ; n = 2 GD( E) it holds that ....

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W. Marek and M. Truszczynski. Nonmonotonic Logics { Context-Dependent Reasoning. Springer, 1993.

....to logic programming. Autoepistemic logic is among the most extensively studied nonmonotonic formal systems. It is closely related to default logic introduced by Reiter in [17] It can handle default reasonings under a simple and modular translation in the case of prerequisite free defaults [10]. In the case of arbitrary default theories, a somewhat more complex non modular translation provides a oneto one correspondence between default extensions and stable (autoepistemic) expansions [5] Further, under the so called Gelfond translation, autoepistemic logic captures the semantics of ....

.... expansions [5] Further, under the so called Gelfond translation, autoepistemic logic captures the semantics of stable models for logic programs [3] Under the Konolige encoding [6] of logic programs as modal theories, stable expansions generalize the concept of the supported model semantics [10]. 2 M. Denecker, V.W. Marek and M. Truszczynski Autoepistemic logic is also known to be equivalent to several other modal nonmonotonic reasoning systems including the only knowing logic of Levesque [8] and the reflexive autoepistemic logic of Schwarz [18] The semantics for autoepistemic logic ....

[Article contains additional citation context not shown here]

W. Marek and M. Truszczy'nski. Nonmonotonic logics; context-dependent reasoning. Springer-Verlag, Berlin, 1993.

No context found.

Viktor M. Marek and Mirek Truszczynski. Nonmonotonic Logics; Context-Dependent Reasoning. Springer Verlag, Berlin-Heidelberg-New York, 1st edition, 1993.

No context found.

V. M. Marek and M. Truszczynski. Nonmonotonic Logics; Context-Dependent Reasoning. Springer Verlag, Berlin-Heidelberg-New York, 1st edition, 1993.

No context found.

V. W. Marek and M. Truszczynski. Nonmonotonic Logic, context-dependent reasoning. Springer-Verlag, 1993.

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