297 research outputs found
Positive Logic with Adjoint Modalities: Proof Theory, Semantics and Reasoning about Information
We consider a simple modal logic whose non-modal part has conjunction and
disjunction as connectives and whose modalities come in adjoint pairs, but are
not in general closure operators. Despite absence of negation and implication,
and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and
S5, such logics are useful, as shown in previous work by Baltag, Coecke and the
first author, for encoding and reasoning about information and misinformation
in multi-agent systems. For such a logic we present an algebraic semantics,
using lattices with agent-indexed families of adjoint pairs of operators, and a
cut-free sequent calculus. The calculus exploits operators on sequents, in the
style of "nested" or "tree-sequent" calculi; cut-admissibility is shown by
constructive syntactic methods. The applicability of the logic is illustrated
by reasoning about the muddy children puzzle, for which the calculus is
augmented with extra rules to express the facts of the muddy children scenario.Comment: This paper is the full version of the article that is to appear in
the ENTCS proceedings of the 25th conference on the Mathematical Foundations
of Programming Semantics (MFPS), April 2009, University of Oxfor
Tense distributive lattices: algebra, logic and topology
Tense logic was introduced by Arthur Prior in the late 1950s as a result of
his interest in the relationship between tense and modality. Prior's idea was
to add four primitive modal-like unary connectives to the base language today
widely known as Prior's tense operators. Since then, Prior's operators have
been considered in many contexts by different authors, in particular, in the
context of algebraic logic.
Here, we consider the category tdlat of bounded distributive lattices
equipped with Prior's tense operators. We establish categorical dualities for
tdlat in terms of certain categories of Kripke frames and Priestley spaces,
respectively. As an application, we characterize the congruence lattice of any
tense distributive lattice as well as the subdirectly irreducible members of
this category. Finally, we define the logic that preserves degrees of truth
with respect to tdlat-algebras and precise the relation between particular
sub-classes of tdlat and know tense logics found in the literature
State-of-the-art on evolution and reactivity
This report starts by, in Chapter 1, outlining aspects of querying and updating resources on
the Web and on the Semantic Web, including the development of query and update languages
to be carried out within the Rewerse project.
From this outline, it becomes clear that several existing research areas and topics are of
interest for this work in Rewerse. In the remainder of this report we further present state of
the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give
an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs;
in Chapter 4 event-condition-action rules, both in the context of active database systems and
in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks
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