Ecumenical modal logic

The discussion about how to put together Gentzen's systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called Ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz' system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz' main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In a recent work, Ecumenical sequent calculi and a nested system were presented, and some very interesting proof theoretical properties of the systems were established. In this work we extend Prawitz' Ecumenical idea to alethic K-modalities

Multi-Agent Only-Knowing Revisited

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic constructs in the semantics and needs to axiomatize validity as part of the logic. It is also not clear how to generalize their ideas to a first-order case. In this paper, we propose a new account of multi-agent only-knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. We then provide, for the propositional fragment, a sound and complete axiomatization that faithfully lifts Levesque's proof theory to the many agent case. We also discuss comparisons to the earlier approach by Halpern and Lakemeyer.Comment: Appears in Principles of Knowledge Representation and Reasoning 201

An ontology for software component matching

The Web is likely to be a central platform for software development in the future. We investigate how Semantic Web technologies, in particular ontologies, can be utilised to support software component development in a Web environment. We use description logics, which underlie Semantic Web ontology languages such as DAML+OIL, to develop an ontology for matching requested and provided components. A link between modal logic and description logics will prove invaluable for the provision of reasoning support for component and service behaviour

A semantical framework for the orchestration and choreography of web services

Web Services are software services that can be advertised by providers and invoked by customers using Web technologies. This concept is currently carried further to address the composition of individual services through orchestration and choreography to services processes that communicate and interact with each other. We propose an ontology framework for these Web service processes that provides techniques for their description, matching, and composition. A description logic-based knowledge representation and reasoning framework provides the foundations. We will base this ontological framework on an operational model of service process behaviour and composition

Counterpart semantics for a second-order mu-calculus

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of

Conditionals and modularity in general logics

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics