Carlos Caleiro

Fibring of logics as a categorial construction

Much attention has been given recently to the mechanism of fibring of logics, allowing free mixing of the connectives and using proof rules from both logics. Fibring seems to be a rather useful and general form of combination of logics that deserves detailed study. It is now well understood at the proof-theoretic level. However, the semantics of fibring is still insufficiently understood. Herein we provide a categorial definition of both proof-theoretic and model-theoretic fibring for logics without terms. To this end, we introduce the categories of Hilbert calculi, interpretation systems and logic system presentations. By choosing appropriate notions of morphism it is possible to obtain pure fibring as a coproduct. Fibring with shared symbols is then easily obtained by cocartesian lifting from the category of signatures. Soundness is shown to be preserved by these constructions. We illustrate the constructions within propositional modal logic.

Logics for specifying concurrent information systems

This chapter concentrates on a challenging problem of information system specification and design, namely how to cope on a high level of abstraction with concurrent behaviour and communication as implied by distribution. Since distributed information systems are reactive and open systems maintaining data bases and applications, it is crucial to develop high-level specification techniques that can cope with data and programs as well as with concurrent workflow and communication issues. Techniques from conceptual modeling, abstract data types, concurrent processes and communication protocols are relevant and have to be combined. In the approach presented here, temporal logic is used for specifying sequential object behaviour, and communication facilities are added for specifying interaction between concurrent objects. We study two distributed temporal logics dealing with communication in two different ways. D0 adds basic statements that can only express synchronous “calling” of predicates, while D1 adds much richer facilities for making local statements about other objects in their respective local logics. D0 is more operational and can be animated or implemented more easily, while D1 is intuitively more appealing and convenient for modeling and specification. We demonstrate by example how D1 can be effectively reduced to D0 in a sound and complete way.

Fibring Non-Truth-Functional Logics: Completeness Preservation

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established.

Specifying communication in distributed information systems

Abstract. We present two logics that allow specifying distributed information systems, emphasizing communication among sites. The low-level logic

Metareasoning about Security Protocols using Distributed Temporal Logic

\mbox{\sf D}_0

Relating Strand Spaces and Distributed Temporal Logic for Security Protocol Analysis

offers features that are easy to implement but awkward to use for specification, while the high-level logic

Synchronization of logics

\mbox{\sf D}_1

Parameterisation of Logics

offers convenient specification features that are not easy to implement. We show that

Deconstructing Alice and Bob

\mbox{\sf D}_1

Combining Logics: Parchments Revisited

specifications may be automatically translated to