Notes on Nonmonotonic Autoepistemic Propositional Logic
This paper comprises an in-depth study of semantics of autoepistemic logic that is based on author’s may years of research in the subject matter. It begins with a brief review of semantics of common patterns of nonmonotonic deduction arising from a lack of knowledge, including autoepistemic deduction, in terms of the fixed-point equation φ(T,E)=E. Then it narrowly investigates minimal expansion semantics for autoepistemic propositional logic and its „only knowing” consequence operation CnAE. In particular, the following minimalknowledge assumption MKA : ϕ∈MKA(T) iff ϕ does not add modally positive S5- consequences to T is used to syntactically characterize the operation CnAE by means of suitable completeness theorem. The paper also offers a proof that the consequence operation CnS5 of modal logic S5 is the maximal monotonic consequence operation satisfying CnS5(T)⊆MKA(T) for every modal theory T..
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2011 |
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| Erschienen: |
2011 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:5 |
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| Enthalten in: |
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki - 5(2011), 6, Seite 74-93 |
| Sprache: |
Englisch ; Polnisch |
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| Beteiligte Personen: |
Marek A. Suchenek [VerfasserIn] |
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| Links: |
doi.org [kostenfrei] |
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| Themen: |
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| doi: |
10.26348/znwwsi.6.74 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
DOAJ046772162 |
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| 520 | |a This paper comprises an in-depth study of semantics of autoepistemic logic that is based on author’s may years of research in the subject matter. It begins with a brief review of semantics of common patterns of nonmonotonic deduction arising from a lack of knowledge, including autoepistemic deduction, in terms of the fixed-point equation φ(T,E)=E. Then it narrowly investigates minimal expansion semantics for autoepistemic propositional logic and its „only knowing” consequence operation CnAE. In particular, the following minimalknowledge assumption MKA : ϕ∈MKA(T) iff ϕ does not add modally positive S5- consequences to T is used to syntactically characterize the operation CnAE by means of suitable completeness theorem. The paper also offers a proof that the consequence operation CnS5 of modal logic S5 is the maximal monotonic consequence operation satisfying CnS5(T)⊆MKA(T) for every modal theory T. | ||
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