It was shown in [6] that the at Rescher{Manor consequence relations| the Free, Strong, Argued, C-Based, and Weak consequence relation|are all characterized by special applications of inconsistency-adaptive logics dened from the paraconsistent logic CLuN. As as result, these consequence relations are provided with a dynamic proof theory. In the present paper we show that the detour via an inconsistency-adaptive logic is not necessary. We present a direct dynamic proof theory, formulated in the language of Classical Logic, and prove its adequacy. 1 Aim of this Paper Rescher{Manor consequence relations constitute an approach to handling inconsistency. The underlying idea is that inconsistent sets of sentences are divided into maximal consistent subsets|henceforth MCS|and that what `follows ' from the inconsistent set is dened in terms of the classical consequences of the MCS or of a selection of them|Classical Logic will henceforth be abbreviated as CL. Such consequence relati...

Penalty logic, introduced by Pinkas [?], associates to each formula of a knowledge base the price to pay if this formula is violated. Penalties may be used as a criterion for selecting preferred consistent subsets in an inconsistent knowledge base, thus inducing a nonmonotonic inference relation. A precise formalization and the main properties of penalty logic and of its associated non-monotonic inference relation are given in the first part. We also show that penalty logic and DempsterShafer theory are related, especially in the infinitesimal case. 1 Introduction The problem of inconsistency handling appears when the available knowledge base -- KB for short -- (here a set of propositional formulas) is inconsistent. Most approaches come up with the inconsistency by selecting among the consistent subsets of KB some preferred subsets; the selection criterion generally makes use of uncertainty considerations, sometimes by using explicitly uncertainty measures (such as Wilson [?], Benfer...

This paper provides an update semantics for counterfactual conditionals. It does so by giving a dynamic twist to the ‘Premise Semantics ’ for counterfactuals developed in Veltman (1976) and Kratzer (1981). It also offers an alternative solution to the problems with naive Premise Semantics discussed by Angelika Kratzer in ‘Lumps of Thought ’ (Kratzer, 1989). Such an alternative is called for given the triviality results presented in Kanazawa et al. (2005, this issue). 1

We develop a conceptual and formal clarification of the notion of surprise as a belief-based phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of the cognitive processing and involves particular kinds of epistemic representations (representations and expectations under scrutiny, implicit beliefs, presuppositions). We define two main kinds of surprise: mismatch-based surprise and astonishment. In the central part of the paper we suggest how a formal model of surprise can be integrated with a formal model of belief change. We investigate the role of surprise in triggering the process of belief reconsideration. There are a number of models of surprise developed in psychology of emotion. We provide several comparisons of our approach with those models.

A logic of diagnosis proceeds in terms of a set of data and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from [26] and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

Contents 0.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 0.2 Pearl's system Z : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 0.2.1 Deriving a natural ordering of defaults : : : : : : : : : : : : : 5 0.2.2 System Z + : resolving remaining ambiguities by explicit means 7 0.3 Conditional entailment : : : : : : : : : : : : : : : : : : : : : : : : : 8 0.4 The argument-based system of Simari and Loui : : : : : : : : : : : : 11 0.5 Brewka's preferred subtheories : : : : : : : : : : : : : : : : : : : : 16 0.6 Ordered logic and basic defeasible logic : : : : : : : : : : : : : : : : 19 0.6.1 Implicit version of Nute's basic defeasible logic : : : : : : : : 20 0.6.2 Ordered logic : : : : : : : : : : : : : : : : : : : : : : : : : 24 0.6.3 Explicit version of Nute's basic defeasible lo

. We formalize several ways of accounting, in the context of logically closed theories, for foundationalist intuitions that underlie change operations applying to belief bases. A positive and a negative concept of entrenchment is defined on the basis of the structure of a given, possibly prioritized belief base. Only the latter, more fine-grained concept proves to be appropriate for a successful attempt at approximating base changes on the theory level. We investigate the question as to which degree we can comply with the fundamental intuition expressed by the various Filtering Conditions that say that all (and only) beliefs that are believed "just because" a retracted belief was believed should be withdrawn. 1 Introduction The problem dealt with in the present paper is best illustrated by an example. Example 1. Consider a theory K = Cn(#, #) which we want to contract with respect to #. Assume that K is generated by the belief base H = {#, #} and that # enjoys epistemic priority ...

........................................................................................................................................................ 2 1 Introduction ............................................................................................................................................ 3 2 Nave dialectical arguments ................................................................................................................... 4 2.1 The structure of nave dialectical arguments............................................................................... 5 2.2 Evaluating nave dialectical arguments....................................................................................... 6 3 DEFLOG's language, interpretations and models .................................................................................... 8 4 Extensions as interpretations of defeasible theories ............................................................................. 12 5 Stages ...

Ranking functions, having their first appearance under the name „ordinale Konditionalfunktionen “ in my Habilitationsschrift submitted in 1983, had several precursors of which I was only incompletely aware, among them Shackle’s functions of potential surprise (see Shackle 1969), Rescher’s plausibility indexing (see Rescher 1976), Adams ’ ε-semantics (see Adams 1975), Cohen’s inductive probabilities (see Cohen 1977), Shafer’s consonant belief functions (see Shafer

The study of paraconsistent inference is the study of inference which prohibits reasoning from inconsistent premises to arbitrary conclusions. In this paper we examine a family of syntax based paraconsistent inference relations and introduce a novel way to study and compare these relations in terms of their preservational properties. 1