Marek, W., and Truszczy nski, M. 1993. Nonmonotonic Logics: Context-Dependent Reasoning. Springer.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....04109 Leipzig, Germany brewka informatik.uni leipzig.de June 28, 2000 0.1. INTRODUCTION 1 0.1 Introduction Commonsense reasoning is nonmonotonic, that is, additional information may invalidate former conclusions. Numerous logics have been proposed which model such forms of reasoning (see [11, 6, 1, 17] for overviews) these logics have been applied to various application problems like reasoning about action, diagnosis, legal reasoning and the like, and in the meantime serious systems implementing subsets of the logics are around, e.g. XSB [16] smodels [12] or dlv [10] In the formalisms ....

Marek, W., Truszczy'nski, M., Nonmonotonic Logics -- ContextDependent Reasoning. Springer, 1993.

....in practice, e.g. methods working for moderately sized instances of NP complete problems do not work for 2 complete problems. The complexity of the problems we are interested in has been extensively studied for existing logics for default reasoning under the standard, stability semantics [3, 15, 23, 19, 29, 2, 10]. Table 1 gives a partial summary of these results for the different logics. We note here that the semantics of circumscription has been originally proposed with respect to sceptical reasoning only. In this case, as shown in [1] reasoning in circumscription (restricted to Herbrand models) ....

Victor W. Marek and Miroslaw Truszczynski. Nonmonotonic logic: contextdependent reasoning. Springer-Verlag, Berlin, Heidelberg, New York, 1993.

....semantics. Among them, the two leading ones are well founded semantics (WFS) 30] and stable model semantics [31] Some OLP programs do not have a stable model, and some have more than one. Furthermore, even for a propositional program, determining whether it has a stable model is NP90 complete [55]. On the other hand, WFS assigns a unique three valued model to every OLP program. For a finite ground program, the complexity of computing its wellfounded model is worst case quadratic in the its size. Mainly because of these behavior and computational complexity features of WFS, the previous ....

W. Marek and M. Trusczynski, Nonmonotonic Logic -- Context-Dependent Reasoning, Springer, Berlin, 1993.

....and cumulativity for well de ned and strati ed default theories. To compute the newly de ned entailment relation, we transform default theories with speci city into semantically equivalent Reiter s default logic (for a collection of algorithms for Reiter s default logic, the reader can consult [29]) We also show that computing the entailment relation of a default theory is at least NP hard. This inspires us to nd sound approximation for this entailment relation which can be computed in polynomial time for the class of default networks which covers the class of acyclic inheritance ....

....default logic such as computing an extension or all extensions of a Reiter s default theory, etc. We achieve that by translating each default theory T into an equivalent Reiter s default theory R T . Before giving the transformation let us recall some basic notion of Reiter s default logic [29, 36, 44]. A R default is a rule of the form : 1 ; n where ; i (i = 1; n) and are rst order formulas. A R default theory is a pair (W; D) where W is a rst order theory and D is a set of R defaults. Let (W; D) be a R default theory, S be a set of formulas. S) is the ....

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W. Marek and M. Truszczynski. Nonmonotonic Logic: Context dependent reasoning. Springer Verlag, 1993.

....concerned with much stronger equivalence properties, involving additional minimality criteria, because our goal is to reconstruct the answer sets of the original programs from the translated ones. Furthermore, we note that our translations amount to semi representability results in the sense of [25], insofar as we embed a full fledged formalism into one of its (syntactically) restricted fragments by means of language extension. With the particular labeling technique employed here, our translation avoids the risk of an exponential blow up in the worst case, faced by a previous approach of ....

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

....from rules. These observations led to the well known stable model semantics for logic programs due to Gelfond and Lifschitz [37] which in turn was shown to have strong equivalences with the classical nonmonotonic reasoning paradigms such as default logic [78] and auto epistemic logic[71] see [38, 65]) as well as numerical reasoning paradigms such as linear programming and integer programming [14, 15] Second, the presence of derivation by contraposition may have a detrimental effect on the complexity of programs, since it inherently simulates disjunction. Therefore, it is advisable to have ....

....Pg is a stable model of P . It is important to observe that by this correspondence, we obtain alternative proofs for the complexity results on reasonable status sets in the previous section. This is because the complexity results known for non monotonic logic programs with stable model semantics [44, 65] directly imply the above results. 5.11 Discussion Thus far, in this section, we have shown that given any logic program P , we can convert P into an agent program , AG(P ) together with associated action base and empty sets of integrity constraints and action constraints) such that: 49 1. ....

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

.... A number of nonmonotonic logics and formalisms have been proposed in the past decades for capturing common sense reasoning, including major formalisms such as circumscription [67, 65] default logic [82] Doyle and McDermott s nonmonotonic logics [69, 68] and Moore s autoepistemic logic [70] see [66]. The computational complexity of nonmonotonic logics has been studied in many papers, e.g. 56, 87, 50, 74, 33, 21, 77] to mention a few comprehensive studies, and is quite well understood. As in the case of belief revision, the complexity of most of these logics resides at the second level of ....

....by default rules of the form : M 1 ; M n which read if is provable and each of 1 ; n can be consistently assumed (i.e. does not lead to contradiction) then conclude that is provable. Many variants and refinements of this approach have been developed, see e.g. [66]. In [56, 87] a rich taxonomy of classes of default rules : M has been defined, by imposing syntactic conditions on their constituents , and and on the structure of the set of defaults. Syntactically, our class of literal Horn defaults corresponds to the class of Horn defaults in ....

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

....j 2 Dg that appear in D. The semantics of a default theory hD; T i is determined by its extensions, i.e. sets of conclusions that are propositionally closed theories associated with hD; T i. Rather than presenting Reiter s de nition of extensions [22] we resort to one by Marek and Truszczyski [16]. The justi cations of a set of defaults are interpreted as follows. For any E L, the reduct DE contains an (ordinary) inference rule whenever there is a default 2 D such that E i for all i 2 f1; ng. Given T L and a set of inference rules R in L, we let (T ) denote the ....

....denote the closure of T under R and propositional consequence. More precisely, the closure Cn (T ) is the least theory T L satisfying (i) T T (ii) for every rule 2 R, 2 T implies 2 T , and (iii) Cn(T . The closure Cn (T ) can be characterized using a proof system [11, 16]. A sentence is R provable from T if there is a sequence 1 1 ; of rules from R such that T [ f 1 ; i 1 g j= i for all i 2 f1; ng and T [ f 1 ; n g j= Then 2 L is R provable from T , 2 Cn (T ) The de nition of extensions follows. De nition ....

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W. Marek and M. Truszczyski. Nonmonotonic Logic: Context-Dependent Reasoning. Springer-Verlag, Berlin, 1993.

....first round of applying beliefs, it treats beliefs and desires analogously. 5.3. Broersen et.al. s BOID architecture The iterative procedure of the BOID architecture given in [BRO 01] is presented as an extension of Reiter s more intuitive characterization of extensions in Theorem 3. Like in [MAR 93] we assume that there is an order on the rules, which we represent by . Finally it is assumed that the number of rules is finite. 3 Definition 8 (BOID social stable agents) Let E L be a set of closed wffs, let T = hW; B; O; I ; Di be a closed BOID theory and let be a function from the ....

MAREK V., TRUSZCZYNSKI M., Nonmonotonic logic: Context-dependent reasoning, Springer, Berlin, 1993.

....and cumulativity for well de ned and strati ed default theories. To compute the newly de ned entailment relation, we transform default theories with speci city into semantically equivalent Reiter s default logic (for a collection of algorithms for Reiter s default logic, the reader can consult [24]) We prove that the complexity of the translation algorithm is polynomial in the size of the given default theory. The paper is organized as follows. We rst argue that in inheritance reasoning, speci city between defaults is conditional thus can not be used unconditionally (Section 2) In ....

....words, the translation preserves the semantics of default theories. Moreover, the translation is modular and polynomial, i.e. R T can be modularly constructed and has a size polynomial in the size of T . Before presenting the translation let us recall some basic notion of Reiter s default logic [24, 31, 36]. A R default is a rule of the form : 1 ; n where ; i (i = 1; n) and are rst order formulas which are referred as the prerequisite, the justi cation, and the consequent of the rule, respectively. A R default theory is a pair (W; D) where W is a rst order theory ....

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W. Marek and M. Truszczynski. Nonmonotonic Logic: Context Dependent Reasoning. Springer Verlag, 1993. 39

....W and satisfies the condition: if a : b 1 ; b n =c 2 D, a 2 S 0 and :b i 62 S then c 2 S 0 . Default theories possessing at least one extension will be called coherent. We will later use the following notion of a default proof. A similar notion was also used by Marek and Truszczynski [12]: Definition 2.1. Let T = D; W ) be a default theory, D 0 D, and p a formula. A T default proof for p from D 0 is a finite sequence (d 1 ; d n ) of defaults in D 0 such that the following conditions are satisfied: 1. W [ fcons(d 1 ) cons(d i Gamma1 )g pre(d i ) for ....

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

....task is to find the relations between input and output concepts in a trained network, in the sense that certain inputs cause a particular output. We argue that neural networks are nonmonotonic systems, i.e. they jump to conclusions that might be withdrawn when new information is available [21]. Thus, the set of rules extracted may contain default negation (#) Each neuron can represent a concept or its classical negation ( Consequently, we expect to extract a set of rules of the form: L 1 , L n , #L n 1 , #Lm # Lm 1 , where each L i is a literal (a propositional variable ....

W. Marek, M. Truszczynski, Nonmonotonic Logic: Context Dependent Reasoning, Springer, Berlin,

....2 INFSYS RR 1843 02 01 1 Introduction Handling preference information plays an important role in applications of knowledge representation and reasoning. In the context of logic programs and related formalisms, numerous approaches for adding preference information have been proposed, including [1, 4, 5, 8, 11, 12, 18, 22, 24, 25, 27, 29] to mention some of them. These approaches have been designed for purposes such as capturing specificity or normative preference; see e.g. 7, 11, 25] for reviews and comparisons. The following example is a classical situation for the use of preference information. Example 1 (bird penguin) ....

V.W. Marek and M. Truszczynski. Nonmonotonic Logics -- Context-Dependent Reasoning. SpringerVerlag, 1993.

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Marek, W., and Truszczy nski, M. 1993. Nonmonotonic Logics: Context-Dependent Reasoning. Springer.

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

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Marek, V., and Truszczy nski, M. 1993. Nonmonotonic logic: context-dependent reasoning. Artifical Intelligence. Springer-Verlag.

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V. Marek and M. Truszczy nski. Nonmonotonic logic: contextdependent reasoning. Artifical Intelligence. Springer-Verlag, 1993.

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V. Marek and M. Truszczynski. Nonmonotonic logic: context-dependent reasoning. Artifical Intelligence. Springer Verlag, 1993.

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V. Marek and M. Truszczy nski. Nonmonotonic logic: context-dependent reasoning. Artifical Intelligence. Springer-Verlag, 1993.

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V. Marek and M. Truszczynski. Nonmonotonic logic: context-dependent reasoning. Artifical Intelligence. Springer Verlag, 1993.

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MAREK V., TRUSZCZYNSKI M., Nonmonotonic logic: Context-dependent reasoning, Springer, Berlin, 1993.

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V. Marek and M. Truszczynski. Nonmonotonic logic: context-dependent reasoning. Artifical Intelligence. Springer-Verlag, 1993.

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V.W. Marek, 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, 1993.

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Victor W. Marek and Miroslaw Truszczynski. Nonmonotonic logic: context-dependent reasoning. Springer-Verlag, Berlin, Heidelberg, New York, 1993.

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