Model states revisited:
Abstract: "Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Passau
1995
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| Schriftenreihe: | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP
1995,22 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the logic program. Replacing logic programs by the more general disjunctive logic programs where we admit disjunctions in the head of rules we have the following situation. However, a disjunctive fact has several different minimal Herbrand models. Hence, disjunctive logic programs posess in general a set of minimal Herbrand models, the minimal model semantics. To obtain an analogous fixpoint characterization one has to collect the Herbrand structures into one object. Therefore Lobo, Minker, Rajasekar (cf.[5]) have introduced the notion of a model state of a disjunctive logic program where disjunctions of ground goals replace the ground goals. -- However, a small counterexample shows that their definition needs to be corrected. In this paper we introduce an improved definition and develop carefully the correspondence between states and their saet [sic] of structures. As a pay-off we obtain a generalization of the results to states for 3-valued Herbrand structures. Since 3-valued Herbrand structures are described by negated and unnegated ground goals, the generalized Herbrand states consist of disjunctions of negated and unnegated ground goals. The 3-valued minimal model semantics yields a minimal-maximal model semantics of Herbrand structures." |
| Beschreibung: | 7, 3 S. |
Internformat
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| 490 | 1 | |a Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |v 1995,22 | |
| 520 | 3 | |a Abstract: "Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the logic program. Replacing logic programs by the more general disjunctive logic programs where we admit disjunctions in the head of rules we have the following situation. However, a disjunctive fact has several different minimal Herbrand models. Hence, disjunctive logic programs posess in general a set of minimal Herbrand models, the minimal model semantics. To obtain an analogous fixpoint characterization one has to collect the Herbrand structures into one object. Therefore Lobo, Minker, Rajasekar (cf.[5]) have introduced the notion of a model state of a disjunctive logic program where disjunctions of ground goals replace the ground goals. -- However, a small counterexample shows that their definition needs to be corrected. In this paper we introduce an improved definition and develop carefully the correspondence between states and their saet [sic] of structures. As a pay-off we obtain a generalization of the results to states for 3-valued Herbrand structures. Since 3-valued Herbrand structures are described by negated and unnegated ground goals, the generalized Herbrand states consist of disjunctions of negated and unnegated ground goals. The 3-valued minimal model semantics yields a minimal-maximal model semantics of Herbrand structures." | |
| 650 | 4 | |a Disjunction (Logic) | |
| 650 | 4 | |a Herbrand's theorem (Number theory) | |
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Datensatz im Suchindex
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| building | Verbundindex |
| bvnumber | BV010602223 |
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| ctrlnum | (OCoLC)36067065 (DE-599)BVBBV010602223 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV010602223 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007071634 |
| oclc_num | 36067065 |
| open_access_boolean | |
| owner | DE-154 DE-739 DE-12 DE-384 DE-91G DE-BY-TUM DE-634 |
| owner_facet | DE-154 DE-739 DE-12 DE-384 DE-91G DE-BY-TUM DE-634 |
| physical | 7, 3 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series2 | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |
| spelling | Volger, Hugo Verfasser aut Model states revisited H. Volger Passau 1995 7, 3 S. txt rdacontent n rdamedia nc rdacarrier Universität <Passau> / Fakultät für Mathematik und Informatik: MIP 1995,22 Abstract: "Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the logic program. Replacing logic programs by the more general disjunctive logic programs where we admit disjunctions in the head of rules we have the following situation. However, a disjunctive fact has several different minimal Herbrand models. Hence, disjunctive logic programs posess in general a set of minimal Herbrand models, the minimal model semantics. To obtain an analogous fixpoint characterization one has to collect the Herbrand structures into one object. Therefore Lobo, Minker, Rajasekar (cf.[5]) have introduced the notion of a model state of a disjunctive logic program where disjunctions of ground goals replace the ground goals. -- However, a small counterexample shows that their definition needs to be corrected. In this paper we introduce an improved definition and develop carefully the correspondence between states and their saet [sic] of structures. As a pay-off we obtain a generalization of the results to states for 3-valued Herbrand structures. Since 3-valued Herbrand structures are described by negated and unnegated ground goals, the generalized Herbrand states consist of disjunctions of negated and unnegated ground goals. The 3-valued minimal model semantics yields a minimal-maximal model semantics of Herbrand structures." Disjunction (Logic) Herbrand's theorem (Number theory) Logic programming Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Fakultät für Mathematik und Informatik: MIP Universität <Passau> 1995,22 (DE-604)BV000905393 1995,22 |
| spellingShingle | Volger, Hugo Model states revisited Disjunction (Logic) Herbrand's theorem (Number theory) Logic programming Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4026894-9 (DE-588)4037944-9 |
| title | Model states revisited |
| title_auth | Model states revisited |
| title_exact_search | Model states revisited |
| title_full | Model states revisited H. Volger |
| title_fullStr | Model states revisited H. Volger |
| title_full_unstemmed | Model states revisited H. Volger |
| title_short | Model states revisited |
| title_sort | model states revisited |
| topic | Disjunction (Logic) Herbrand's theorem (Number theory) Logic programming Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Disjunction (Logic) Herbrand's theorem (Number theory) Logic programming Theoretische Informatik Informatik Mathematik |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT volgerhugo modelstatesrevisited |