We present a compositional program logic for call-by-value imperative higherorder functions with general forms of aliasing, which can arise from the use of reference names as function parameters, return values, content of references and part of data structures. The program logic

Abstract. We investigate the computational complexity of reasoning over various fragments of the Extended Entity-Relationship (EER) language, which includes a number of constructs: ISA between entities and relationships, disjointness and covering of entities and relationships, cardinality constraints for entities in relationships and their refinements as well as multiplicity constraints for attributes. We extend the known EXPTIME-completeness result for UML class diagrams [5] and show that reasoning over EER diagrams with ISA between relationships is EXPTIME-complete even without relationship covering. Surprisingly, reasoning becomes NP-complete when we drop ISA between relationships (while still allowing all types of constraints on entities). If we further omit disjointness and covering over entities, reasoning becomes polynomial. Our lower complexity bound results are proved by direct reductions, while the upper bounds follow from the correspondences with expressive variants of the description logic DL-Lite, which we establish in this paper. These correspondences also show the usefulness of DL-Lite as a language for reasoning over conceptual models and ontologies.

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more

We show that there exist 2^ℵ0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames. The constructions use the result of Erd os that there are finite graphs with arbitrarily large chromatic number and girth.

Abstract. Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language L ′ is the least expressive extension of L with interpolation. For instance, let M(D) be the extension of the basic modal language with a difference operator [7]. First-order logic is the least expressive extension of M(D) with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment. §1. Introduction. In this paper, we consider extensions of the basic modal language that involve reference to individual states of a Kripke structure. A typical example is the language H(E), in which one can refer to individual states of the Kripke model using nominals (similar to constants in first-order logic) and the universal modality [9]. Another example is difference logic M(D), i.e.,

Abstract. Multi-agent environments comprise decision makers whose deliberations involve reasoning about the expected behavior of other agents. Apposite concepts of rational choice have been studied and formalized in game theory and our particular interest is with their integration in a logical specification language for multiagent systems. This paper concerns the logical analysis of the gametheoretical notions of a (subgame perfect) Nash equilibrium and that of a (subgame perfect) best response strategy. Extensive forms of games are conceived of as Kripke frames and a version of Propositional Dynamic Logic is employed to describe them. We show how formula schemes of our language characterize those classes of frames in which the strategic choices of the agents can be said to be Nashoptimal. Our analysis focuses on extensive games of perfect information without repetition. 1

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIMEcomplete in the multiagent case, both for the deliberative and Chellas’s STIT. 1

We show how to extend O’Hearn and Pym’s logic of bunched implications, BI, to classical BI (CBI), in which both the additive and the multiplicative connectives behave classically. Specifically, CBI is a non-conservative extension of (propositional) Boolean BI that includes multiplicative versions of falsity, negation and disjunction. We give an algebraic semantics for CBI that leads us naturally to consider resource models of CBI in which every resource has a unique dual. We then give a cut-eliminating proof system for CBI, based on Belnap’s display logic, and demonstrate soundness and completeness of this proof system with respect to our semantics.

The notion of “preference ” has circulated in many disciplines in the first half of the 20th century, especially in economics and social choice theory (cf. [34]). In logic, Halldén [9] initiated a field of research that was quickly championed by G. H. von Wright in [33], a book that is usually taken to be the seminal work in preference logic. The present paper presents a modal logic for the formalization of preferences as initiated by von Wright. Beside historical concerns, a logic of preference finds an independent modern interest in various (sub-)disciplines of economics, social choice theory, computer science and philosophy, to name a few. For instance, it proved indispensable to investigate the logic of solution concepts of game theory such as backward induction and Nash equilibrium (see [30]). Our preference logic can define a strict global binary relation between propositions which has an essential ceteris paribus rider. We achieve the first features with what we call the basic preference language. We start with a reflexive and transitive accessibility relation ≤ over states, where accessible states are those that are at least as good as the present one. To reason about strict preferences, we take the strict subrelation of ≤

This paper contributes to the principled construction of tableau-based decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For converse-free formulas we present a terminating control that does not rely on the usual chain-based blocking scheme. Our tableau systems are based on a new model existence theorem.