We consider an extension of the propositional modal logic S4 which allows <> to act not only on isolated formulas, but also on sets of formulas. The interpretation of <>A is then given by the tangled closure of the valuations of formulas in A, which over finite transitive, reflexive models indicates the existence of a cluster satisfying A. This extension has been shown to be more expressive than the basic modal language: for example, it is equivalent to the bisimulation-invariant fragment of FOL over finite S4 models, whereas the basic modal language is weaker. However, previous analyses of this logic have been entirely semantic, and no proof system was available. In this paper we present a sound proof system for the polyadic S4 and prove that it is complete. The axiomatization is fairly standard, adding only the fixpoint axioms of the tangled closure to the usual S4 axioms. The proof proceeds by explicitly constructing a finite model from a consistent set of formulas.

The concept of "ideal semantics" has been promoted as an alternative basis for skeptical reasoning within abstract argumentation settings. Informally, ideal acceptance not only requires an argument to be skeptically accepted in the traditional sense but further insists that the argument is in an admissible set all of whose arguments are also skeptically accepted. The original proposal was couched in terms of the so-called preferred semantics for abstract argumentation. We argue, in this paper, that the notion of "deal acceptability'' is applicable to arbitrary semantics and justify this claim by showing that standard properties of classical ideal semantics, e.g. unique status, continue to hold in any "reasonable" extension-based semantics. We categorise the relationship between the divers concepts of "ideal extension wrt semantics s" that arise and we present a comprehensive analysis of algorithmic and complexity-theoretic issues.

We compare the expressiveness of the fragments of Halpern and Shoham's interval logic (HS), i.e., of all interval logics with modal operators associated with Allen's relations between intervals in linear orders. We establish a complete set of inter-definability equations between these modal operators, and thus obtain a complete classification of the family of 212 fragments of HS with respect to their expressiveness. Using that result and a computer program, we have found that there are 1347 expressively different such interval logics over the class of all linear orders.

This paper investigates belief revision where the underlying logic is that governing Horn clauses. It proves to be the case that classical (AGM) belief revision doesn’t immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, Horn revision functions in the obvious extension to the AGM approach are not captured by total preorders over possible worlds. We address these difficulties by first restricting the semantic construction to "well behaved" orderings; and second, by augmenting the revision postulates by an additional postulate. This additional postulate is redundant in the AGM approach but not in the Horn case. In a representation result we show that these two approaches coincide. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.

This work develops an approach to efficient reasoning in first-order knowledge bases with incomplete information. We build on Levesque's proper knowledge bases approach, which supports limited incomplete knowledge in the form of a possibly infinite set of positive or negative ground facts. We propose a generalization which allows these facts to involve unknown individuals, as in the work on labeled null values in databases. Dealing with such unknown individuals has been shown to be a key feature in the database literature on data integration and data exchange. In this way, we obtain one of the most expressive first-order open-world settings for which reasoning can still be done efficiently by evaluation, as in relational databases. We show the soundness of the reasoning procedure and its completeness for queries in a certain normal form.

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics, a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is build on top of the classical entailment relation.

Query containment has been studied extensively in KR and databases, for different kinds of query languages and domain constraints. We address the longstanding open problem of containment under expressive description logic (DL) constraints for two-way regular path queries (2RPQs) and their conjunctions, which generalize conjunctive queries with the ability to express regular navigation. We show that, surprisingly, functionality constraints alone make containment of 2RPQs already ExpTime-hard. By employing automata-theoretic techniques, we also provide a matching upper bound that extends to very expressive DL constraints. For conjunctive 2RPQs we prove a further exponential jump in complexity, and provide again a matching upper bound for expressive DLs. Our techniques provide also a solution to the problem of query entailment over DL knowledge bases in which individuals in the ABox may be related through regular role-paths.

The automata-based approach is based on translating a knowledge base (KB) whose satisfiability is to be checked In this work we describe the theoretical foundations into some variant of automata on infinite trees that accepts and the implementation of a new automata-based tree-shaped models of the KB, and checking such an automaton technique for reasoning over expressive Description for non-emptiness. This approach is powerful and flexible. Logics that is worst-case optimal and lends itself It is acknowledged that it provides a very robust basis to an efficient implementation. In order to show for showing worst-case optimal complexity upper bounds, the feasibility of the approach, we have realized a and has been applied for a wide range of expressive DLs working prototype of a reasoner based upon these and reasoning services (cf.

We define an extension of stit logic that encompasses subjective probabilities representing beliefs about simultaneous choice exertion of other agents. The formalism enables us to express the notion of "attempt" as a choice exertion that maximizes the chance of success with respect to an action effect. The notion of attempt (or effort) is central in philosophical and legal discussions on responsibility and liability.

Multi-context systems (MCS) are a powerful framework for interlinking heterogeneous knowledge sources. They model the flow of information among different reasoning components (called contexts) in a declarative way, using so-called bridge rules, where contexts and bridge rules may be nonmonotonic. We considerably generalize MCS to managed MCS (mMCS): while the original bridge rules can only add information to contexts, our generalization allows arbitrary operations on context knowledge bases to be freely defined, e.g., deletion or revision operators. The paper motivates and introduces the generalized framework and presents several interesting instances. Furthermore, we consider inconsistency management in mMCS and complexity issues.