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In this paper we consider distributive modal logic, a setting in which
we may add modalities, such as classical types of modalities as well
as weak forms of negation, to the fragment of classical propositional
logic given by conjunction, disjunction, true, and false. For these
logics we define bo...
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We give a characterization of the simple, and of the subdirectly
irreducible boolean algebras with operators (including modal
algebras), in terms of the dual descriptive frame. These
characterizations involve a special binary \emph{quasi-reachability}
relation on the dual structure; we call a poi...
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We define a nontrivial variety of boolean algebras with operators such
that every member of the variety is atomless. This shows that not
every variety of boolean algebras with operators is generated by its
atomic members, and thus establishes a strong incompleteness result in
(multi-)modal logic.
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Craig's interpolation lemma fails for many propositional and first order
modal logics. The interpolation property is often regarded as a sign of
well-matched syntax and semantics. Hybrid logicians claim that modal logic
is missing important syntactic machinery, namely tools for referring to
...
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Abstract: This paper uses classical logic for a simultaneous
description of the syntax and semantics of a fragment of English and
it is argued that such an approach to natural language allows
procedural aspects of linguistic theory to get a purely declarative
formulation. In particular, it will b...
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We provide a detailed analysis of very weak fragments of modal
logic. Our fragments lack connectives that introduce non-determinism
and they feature restrictions on the modal operators, which may lead
to substantial reductions in complexity. Our main result is a general
game-based characterizati...
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In recent years, an important number of theoretical results concerning
axiomatizability, proof systems (tableaux, natural deduction, etc.),
interpolation, expressive power, complexity, etc. for hybrid logics
has been obtained. The next natural step is to develop provers that
can handle these lan...
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We provide a resolution-based proof procedure for modal, description
and hybrid logic that improves on previous proposals in important
ways. It avoids translation into large undecidable logics, and works
directly on modal, description or hybird logic formulas instead. In
addition, by using the ...
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This paper deals with the logic obtained by extending Kozen
mu-calculus with the so-called `` bisimulation quantifiers''. These
quantifiers allow to look for a subset P satisfying a priperty F(P)
not only within the model, but also in any other model which is
bisimilar to the given one. By usin...
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In the precursor to this report, we investigated the lattice
$\Lambda(Df_2)$ of all subvarieties of the variety $Df_2$ of
two-dimensional diagonal free cylindric algebras. In the present paper
we investigate the lattice $\Lambda(CA_2)$ of all subvarieties of the
variety $CA_2$ of two-dimensional ...
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Data-Oriented Parsing (DOP) models of natural language propose that human
language processing works with representations of concrete past language
experiences rather than with abstract linguistic rules. These models
operate by decomposing the given representations into fragments and
recomposing t...