L. M. Pereira, J. J. Alferes and J. N. Aparicio, The Extended Stable Models of Contradiction Removal Semantics. In: P. Barahona, L.M. Pereira and A. Porto, (eds.), Proceedings-EPIA 91, Springer Verlag, Heidelberg, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to contradictions, as well as those arising from contradictions. The following example provides an intuitive preview of what we intend to capture: Example 6. Consider program P : a b (i) d a (iii) a c (ii) e :a (iv) 7 We treat contradictory programs extending the approach of [27, 28]. 1. b and c hold since there are no rules for either b or c 2. a and a hold from 1 and rules (i) and (ii) 3. a and :a hold from 2 and inference rule (1) cf. page 6) 4. d and e hold from 2 and rules (iii) and (iv) 5. d and e hold from 3 and rules (iii) and (iv) as they are the only ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. In P. Barahona, L. M. Pereira, and A. Porto, editors, EPIA'91, pages 105--119. Springer-Verlag, 1991.

....set of ground literals from the language of a program. We extend the Theta operator[18] from the class of interpretations to the class of p interpretations, and we call this the Theta x operator (x standing for eXtended) 7 We treat contradictory programs extending the approach of [10, 11]. 8 This is not strictly necessary but simplifies the exposition. Furthermore, without loss of generality, we only consider rules L; L for which rules for both L and :L exist in P . We also use the notation L to denote the head of rule L; L. Definition 10 The Theta x operator. ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. In P. Barahona, L. M. Pereira, and A. Porto, editors, EPIA'91, LNAI 541, pages 105--119. Springer--Verlag, 1991.

....general logic programs. Its Extended Stable Models (XSM) 12, 13] version, and the inclusion of a second type of negation, have been explored as a framework for formalizing a variety of forms of non monotonic reasoning [10, 11] and generalized to deal with contradiction removal and counterfactuals [7, 8, 9]. The increasing role of logic programming extensions as an encompassing framework for these and other AI topics is expounded at length in [4] where they argue, and we concur, that WFS is by design overly careful in deciding about the falsity of some atoms, leaving them undefined, and that a ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. In P. Barahona, L. M. Pereira, and A. Porto, editors, 5th Portuguese AI Conference, volume 541 of LNAI, pages 105--119. Springer-Verlag, 1991.

....revisions. Example 5. Let P = fp not q; p not r; a not bg; with Rev = fnot q; not r; not bg. Its submodels lattice is depicted in fig. 1. For simplicity, contradictory models are not presented in full. 7 For a study of submodels based on the XSMs instead of on the well founded model see [7]. p, not p, not q not r, not b p, not p, not r, a, not b not q not q, not r, not b not b p, not p, not q, a, not b not r p, not p, not r not q, not b a, not b not q, not r Fig. 1. Submodels lattice of example 5 As we are interested in revising contradiction ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. In P. Barahona, L. M. Pereira, and A. Porto, editors, 5th Portuguese AI Conf. Springer-Verlag, 1991.

....[ Van Gelder et al. 1980 ] has been proposed as a suitable semantics for general logic programs. Its Extended Stable Models (XSM) Przymusinska and Przymusinski, 1990, Przymusinski, 1990 ] version has been explored as a framework for formalizing a variety of forms of non monotonic reasoning [ Pereira et al. 1991d, Pereira et al. 1991e ] and generalized to deal with contradiction removal and counterfactuals [ Pereira et al. 1991a, Pereira et al. 1991b, Pereira et al. 1991c ] The increasing role of logic programming extensions as an encompassing framework for these and other AI topics is expounded ....

....1980 ] has been proposed as a suitable semantics for general logic programs. Its Extended Stable Models (XSM) Przymusinska and Przymusinski, 1990, Przymusinski, 1990 ] version has been explored as a framework for formalizing a variety of forms of non monotonic reasoning [ Pereira et al. 1991d, Pereira et al. 1991e ] and generalized to deal with contradiction removal and counterfactuals [ Pereira et al. 1991a, Pereira et al. 1991b, Pereira et al. 1991c ] The increasing role of logic programming extensions as an encompassing framework for these and other AI topics is expounded at length in [ Kakas ....

[Article contains additional citation context not shown here]

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. In P. Barahona, L. M. Pereira, and A. Porto, editors, 5th Portuguese AI Conference'91. Springer-Verlag, 1991.

....only if both two conditions below hold: ffl 8l 2 Sup; 9XSS(l) j d RS XSS(l) fg ffl 8XSS( Sup XSS( fg d RS XSS( 6= fg where Sup = CX Gamma M P and d RS is the set of complement of the atoms in RS. Proof of the theorem below is omitted here for brevity, but appears in [PAA91b]. Theorem 5.2 Correctness of the mapping An element belongs to the family [RS] of a program P with WFM M P iff it belongs to the codomain of (M P ; RS) Example 9 Consider the program: p: a b; q: c d: p b; c: b a: d c: p q: whose only CRS is fqg. Its XSMs are: f:p; p; ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. Technical report, AI Centre/Uninova, 1991.

....Their semantics exercises some contradiction removal, giving thus meaning to more programs. To the program of example 2 it assigns the semantics is fag, leaving b undefined. We consider the issue of contradiction removal a separate one and we treat it, differently, elsewhere in the spirit of [9, 10]. 2 Language Used Given a first order language Lang [17] an extended logic program is a set of rules of the form H B 1 ; Bn ; C1 ; Cm , where H; B 1 ; Bn ; C 1 ; Cm are classical literals. A (syntactically) classical literal (or explicit literal) is either ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. The extended stable models of contradiction removal semantics. In P. Barahona, L. M. Pereira, and A. Porto, editors, 5th Portuguese AI Conf.'91. Springer-Verlag, 1991.

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L. M. Pereira, J. J. Alferes and J. N. Aparicio, The Extended Stable Models of Contradiction Removal Semantics. In: P. Barahona, L.M. Pereira and A. Porto, (eds.), Proceedings-EPIA 91, Springer Verlag, Heidelberg, 1991.

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