By Alexander Bochman

ISBN-10: 3642075169

ISBN-13: 9783642075162

ISBN-10: 3662045605

ISBN-13: 9783662045602

The major topic and goal of this ebook are logical foundations of non monotonic reasoning. This bears a presumption that there's this kind of factor as a normal idea of non monotonic reasoning, rather than a number of structures for one of these reasoning latest within the literature. It additionally presumes that this type of reasoning will be analyzed via logical instruments (broadly understood), simply as the other form of reasoning. with a purpose to in achieving our objective, we'll supply a standard logical foundation and semantic illustration during which other forms of non monotonic reasoning will be interpreted and studied. The advised framework will subsume ba sic types of nonmonotonic inference, together with not just the standard skeptical one, but in addition numerous kinds of credulous (brave) and defeasible reasoning, in addition to a few new varieties akin to contraction inference family that specific relative independence of items of knowledge. moreover, an analogous framework will function a foundation for a common thought of trust swap which, between different issues, will let us unify the most ways to trust switch current within the literature, in addition to to supply a optimistic view of the semantic illustration used. This publication 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**

**Example text**

B will be called a base proposition of If- if it is basic and prime. The above condition for basic propositions is a generalized form of a deduction theorem for Scott consequence relations. Consequently, basic propositions are, in a sense, propositions that behave classically in our supraclassical context. The following result provides a semantic characterization of such propositions. 2. A is a basic proposition of II- iff, for any theory u of II-, CI({A}Uu) is also a theory ofll-. Proof. Let u be a theory of II-.

In many applications, however, we will need such a stronger notion of groundedness. 3. A supraclassical Scott consequence relation II- will be called strongly generated by a pair (Ll, Th) if any small theory of II- coincides with Th(D), for some DELl. 1. Again, it turns out that there exists a purely internal characterization of strongly generated consequence relations. 4. A supraclassical Scott consequence relation will be called strongly grounded if all its small theories are prime. 2. A supraclassical consequence relation is strongly grounded iff it is strongly generated by some set of propositions.

Thus w is a theory of If- u , and hence the above condition amounts to aWU b. 0 Primeness. A Scott consequence relation will be called prime if it has a unique least theory. Such consequence relations form an exact dual of determinate consequence relations. The following lemma gives a syntactic description of primeness. 12. A Scott consequence relation is prime iff, for any set a, If- a holds only if If- A, for some A E a. Proof. Assume that If- has a least theory uo. Then, for any proposition A, if W A, then A does not belong to some theory of If-, and consequently it does not belong to uo.

### A Logical Theory of Nonmonotonic Inference and Belief Change by Alexander Bochman

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