In [25] van Benthem proposes a dynamic consequence relation defined as ψ1, . . . , ψn |= φ iff |= [ψ1]...[ψn]φ, where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation |=Γ extending van Benthem’s proposal. It takes into account a set of background conditions...

We propose a novel consequence-based algorithm for TBox reasoning in SHIQ. This work is at very early stage: we have no experimental results and we have not even proved completeness. Instead, we focus on explaining the intuitions behind the algorithm, and show that it has all the favorable properties of existing consequence-based algorithms, namely optimal worst-case complexity, one-pass classi...

Unresolved conflicts can introduce inconsistent and uncertain choices into a system description. Such inconsistencies imply nondeterminancy and nondeterminism is a bad thing; e.g. Leveson says that “nondeterminism is the enemy of reliability” [2]. Requirement engineers, on the other hand, argue that inconsistencies are a good thing [9]. To be human is to hold an opinion. To be an expert is to h...

We explore a connection between different ways of representing information in computer science. We show that relational databases, modules, algebraic specifications and constraint systems all satisfy the same ten axioms. A commutative semigroup together with a lattice satisfying these axioms is then called an “information algebra”. We show that any compact consequence operator satisfying the in...

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined ...

The present paper investigates consequence relations that are both paraconsistent and plausible (generally nonmonotonic too). More precisely, we lay the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations (such as in Non-monotonic Reasoning). The first purpose of the paper is to provide characteri...

1 Consequence Relations A useful notion that cuts across both semantic (model-oriented) and syntactic (derivation-oriented) issues is the notion of a consequence relation. We will use capital Greek letters like Γ,∆ (Gamma and Delta) to refer to finite sets of formulas, and lower case Greek letters like φ, ψ (phi and psi) to refer to individual formulas. We will save ink by writing Γ,∆ for the s...

The purpose of this paper is to explore the notion of consequence in Approximate Reasoning. While logical consequence has an standard (semantic and syntactic) definition in Exact Logic, several different definitions of that concept can be considered in the Approximate Reasoning framework. In this paper some definitions are compared with consequences derived from inference methods used in Artifi...