By Alexander Bochman
The major topic and goal of this booklet are logical foundations of non monotonic reasoning. This bears a presumption that there's any such factor as a normal idea of non monotonic reasoning, in place of a host of structures for the sort of reasoning current within the literature. It additionally presumes that this type of reasoning will be analyzed by way of logical instruments (broadly understood), simply as the other form of reasoning. with a view to in attaining our aim, we are going to offer a typical logical foundation and semantic illustration within which other forms of non monotonic reasoning might be interpreted and studied. The instructed framework will subsume ba sic sorts of nonmonotonic inference, together with not just the standard skeptical one, but additionally a variety of different types of credulous (brave) and defeasible reasoning, in addition to a few new types equivalent to contraction inference kinfolk that specific relative independence of items of knowledge. additionally, a similar framework will function a foundation for a common concept of trust switch which, between different issues, will let us unify the most techniques to trust swap present within the literature, in addition to to supply a optimistic view of the semantic illustration used. This ebook is a monograph instead of a textbook, with all its merits (mainly for the writer) and shortcomings (for the reader).
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Additional resources for A Logical Theory of Nonmonotonic Inference and Belief Change
If B --t c, there must exist Bl E Ll'" such that a <;;; Th(Bd and B --t c <;;; Th(Bd. The later condition implies that c is disjoint from Th(B 1\ Bd. In addition, Th(B 1\ B 1 ) includes both Band a. If c. Therefore, B is a base proposition of 11-. 3. A is a base proposition of a base-generated consequence relation II- if and only if it is prime in II-. Proof. Let II- be a consequence relation generated by a base Ll with respect to Th, and assume that A is prime, that is, Th1f-(A) is a theory of 11-.
The actual conclusions and 1 Notice that we reverse the direction of preference as compared with common representations of non monotonic inference. 46 3. Epistemic States assumptions made by the agent in particular situations will be obtained by combining her epistemic state with available facts. More exactly, such conclusions will be obtained by choosing preferred admissible belief states that are consistent with the facts. An admissible belief state s E S will be said to support a proposition A, if A belongs to its associated belief set, that is, A E l(s).
Actually, in many applications the preference relation of an epistemic state will be obtained in the same way as a strict counterpart of some weak preference relation ~; namely it will defined as s ~ t == s ~ t and t -:/;. s The qualification 'epistemic' in the name of our epistemic states is not accidental. Epistemic states say nothing directly about what is actually true, but only what is believed (or presumed) to hold. They are intended to reflect, in particular, the requirement of separating background and contingent knowledge suggested by several authors (see [Poo9I, Gef92]).
A Logical Theory of Nonmonotonic Inference and Belief Change by Alexander Bochman