A Preferential Model Semantics For Default Logic

@inproceedings{Voorbraak1991APM,
  title={A Preferential Model Semantics For Default Logic},
  author={Frans Voorbraak},
  booktitle={ECSQARU},
  year={1991}
}
Shoham proposed a uniform approach to systems for nonmonotonic reasoning, which consists in considering standard logics augmented with a preference relation on the interpretations. Circumscription can easily seen to be a special case of this preference logic framework, but capturing default logic turned out to be, more difficult, and is even thought to be impossible by some researchers of nonmonotonic reasoning. In this paper a preferential model semantics for default logic is given, by… 
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References

SHOWING 1-10 OF 49 REFERENCES
Interpolation in Fragments of Intuitionistic Propositional Logic
TLDR
The following strong interpolation theorem is proved: if IpL }-A+B and A or B is in NNIL, then there is an interpolant I in KNIT, and this settles a question posed by A. Visser.
The logic of actual obligation. An alternative approach to deontic logic
In this paper we develop a system of deontic logic (LAO, the logic of actual obligation) with a rather limited scope: we are, only interested in obligations as far as they: are relevant for
Applications of constructive logic to sheaf constructions in toposes
The internal logic of a topos is exploited to give an easy proof of the fact that topologies in a topos form a locale and to give simple internal reformulations of two well-known variants of
Peano's Smart Children: A Provability Logical Study of Systems with Built-in Consistency
  • A. Visser
  • Mathematics
    Notre Dame J. Formal Log.
  • 1989
The systems studied in this article prove the same theorems (from the "extensional" point of view) as Peano Arithmetic, but are equipped with a self-correction procedure. These systems prove their
Non-monotonic reasoning : formalization of commonsense reasoning
Elements of monotonic logics foundations of non-monotonic reasoning approaches to non-monotonic reasoning modal non-monotonic logics default logic default logic circumscription approaches to closed
CIRCUMSCRIPTION — A FORM OF NONMONOTONIC REASONING
TLDR
Circumscription formalizes conjectural reasoning that humans and intelligent computer programs must often jump to the conclusion that the objects they can determine to have certain properties or relations are the only objects that do.
Book review: Partiality, Truth and Persistence by Tore Langholm (Lecture Notes 15 Ctr. for the Study of Lang. and Information. University of Chicago Press)
Partiality, Truth and Persistence is the latest in a recent series of inexpensive, softcover lecture notes which deal with various aspects of logic and language. There are several works on natural
Kunnen wij elke machine verslaan?: Beschouwingen rondom Lucas' Argument
In this paper, we discuss Lucas's Argument, which purports to show that there is at least one thing, the producing-as-true of certain Godel sentences, in which we humans are, in principle, superior
Strictness analysis for POLYREC, a language with polymorphic and recursive types
TLDR
This paper defines the functional language POLYREC with polymorphic and recursive types, and develops concrete and abstract interpretations for this language, based on complete partial orderings and complete lattices.
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