This paper is an investigation into the logic of information flow. The basic perspective is that logic flows in virtue of constraints and that constraints classify channels connecting particulars In this paper we explore some logics intended to model reasoning in the case of idealized information flow, that is, where the constraints involved are exceptionless. We look at this as a step toward the far more challenging task of understanding the logic of imperfect information flow, that is where the constraints (...) admit of exceptional connections. This paper continues and amplifies work presented by the same authors in [10]. (shrink)

. The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general (...) structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics. (shrink)

A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula α as the theory defined by the set of all those models of α that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates (...) describe properties of iterated revisions. (shrink)

We discuss several abstract semantics for nonmonotonic logics. We present their motivations, their development and some historical origins, and show that the three systems considered are essentially equivalent: the coherent systems of filters of S. Ben-David and R. Ben-Eliahu, the coherent systems of filters developed by the author, the partial order semantics of N. Friedman and J. Halpern.

This paper introduces a generalization of Reiter’s notion of “extension” for default logic. The main difference from the original version mainly lies in the way conflicts among defaults are handled: in particular, this notion of “general extension” allows defaults not explicitly triggered to pre-empt other defaults. A consequence of the adoption of such a notion of extension is that the collection of all the general extensions of a default theory turns out to have a nontrivial algebraic structure. This fact has (...) two major technical fall-outs: first, it turns out that every default theory has a general extension; second, general extensions allow one to define a well-behaved, skeptical relation of defeasible consequence for default theories, satisfying the principles of Reflexivity, Cut, and Cautious Monotonicity formulated by D. Gabbay. (shrink)

inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to a definition of iaheritance that is..

This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based (...) systems. We also provide a number of examples and consider a rigorous case study, which indicate that our system does not suffer from anomalies. We define consequence relations based on a notion of defeat, consider rationality postulates, and prove that one such consequence relation is consistent. (shrink)