Preferential entailment is a
non-monotonic logic
A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which re ...
based on selecting only
model
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
s that are considered the most plausible. The plausibility of models is expressed by an ordering among models called a preference relation, hence the name preference entailment.
Formally, given a
propositional formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional fo ...
and an ordering over propositional models
, preferential
entailment
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...
selects only the models of
that are minimal according to
. This selection leads to a non-monotonic inference relation:
holds if and only if all minimal models of
according to
are also models of
.
[.]
Circumscription
Circumscription may refer to:
*Circumscribed circle
* Circumscription (logic)
*Circumscription (taxonomy)
*Circumscription theory
The circumscription theory is a theory of the role of warfare in state formation in political anthropology, created ...
can be seen as the particular case of preferential entailment when the ordering is based on containment of the sets of variables assigned to true (in the propositional case) or containment of the extensions of predicates (in the first-order logic case).
See also
*
References
{{reflist
Logic in computer science
Knowledge representation
Non-classical logic