1,945 research outputs found
Inference Rules in some temporal multi-epistemic propositional logics
Multi-modal logics are among the best tools developed so far to analyse
human reasoning and agents’ interactions. Recently multi-modal
logics have found several applications in Artificial Intelligence (AI) and
Computer Science (CS) in the attempt to formalise reasoning about
the behavior of programs. Modal logics deal with sentences that are
qualified by modalities. A modality is any word that could be added to
a statement p to modify its mode of truth. Temporal logics are obtained
by joining tense operators to the classical propositional calculus, giving
rise to a language very effective to describe the flow of time. Epistemic
logics are suitable to formalize reasoning about agents possessing a
certain knowledge. Combinations of temporal and epistemic logics are
particularly effective in describing the interaction of agents through the
flow of time. Although not yet fully investigated, this approach has
found many fruitful applications. These are concerned with the development
of systems modelling reasoning about knowledge and space,
reasoning under uncertainty, multi-agent reasoning et c.
Despite their power, multi modal languages cannot handle a changing
environment. But this is exactly what is required in the case of human
reasoning, computation and multi-agent environment. For this purpose,
inference rules are a core instrument. So far, the research in this
field has investigated many modal and superintuitionistic logics. However,
for the case of multi-modal logics, not much is known concerning
admissible inference rules.
In our research we extend the investigation to some multi-modal propositional logics which combine tense and knowledge modalities. As far
as we are concerned, these systems have never been investigated before.
In particular we start by defining our systems semantically; further we
prove such systems to enjoy the effective finite model property and to
be decidable with respect to their admissible inference rules. We turn
then our attention to the syntactical side and we provide sound and
complete axiomatic systems. We conclude our dissertation by introducing
the reader to the piece of research we are currently working on.
Our original results can be found in [9, 4, 11] (see Appendix A). They
have also been presented by the author at some international conferences
and schools (see [8, 10, 5, 7, 6] and refer to Appendix B for more
details).
Our project concerns philosophy, mathematics, AI and CS. Modern
applications of logic in CS and AI often require languages able to represent
knowledge about dynamic systems. Multi-modal logics serve
these applications in a very efficient way, and we would absorb and
develop some of these techniques to represent logical consequences in
artificial intelligence and computation
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
A Note on Parameterised Knowledge Operations in Temporal Logic
We consider modeling the conception of knowledge in terms of temporal logic.
The study of knowledge logical operations is originated around 1962 by
representation of knowledge and belief using modalities. Nowadays, it is very
good established area. However, we would like to look to it from a bit another
point of view, our paper models knowledge in terms of linear temporal logic
with {\em past}. We consider various versions of logical knowledge operations
which may be defined in this framework. Technically, semantics, language and
temporal knowledge logics based on our approach are constructed. Deciding
algorithms are suggested, unification in terms of this approach is commented.
This paper does not offer strong new technical outputs, instead we suggest new
approach to conception of knowledge (in terms of time).Comment: 10 page
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