319 research outputs found
On expressive power of basic modal intuitionistic logic as a fragment of classical FOL
The modal characterization theorem by J. van Benthem characterizes classical modal logic as the bisimulation invariant fragment of first-order logic. In this paper, we prove a similar characterization theorem for intuitionistic modal logic. For this purpose we introduce the notion of modal asimulation as an analogue of bisimulations. The paper treats four different fragments of first-order logic induced by their respective versions of Kripke-style semantics for modal intuitionistic logic. It is shown further that this characterization can be easily carried over to arbitrary first-order definable subclasses of classical first-order models. © 2016 Elsevier B.V
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
Model-theoretic characterization of predicate intuitionistic formulas
Notions of asimulation and k-asimulation introduced in [Olkhovikov, 2011] are
extended onto the level of predicate logic. We then prove that a first-order
formula is equivalent to a standard translation of an intuitionistic predicate
formula iff it is invariant with respect to k-asimulations for some k, and then
that a first-order formula is equivalent to a standard translation of an
intuitionistic predicate formula iff it is invariant with respect to
asimulations. Finally, it is proved that a first-order formula is equivalent to
a standard translation of an intuitionistic predicate formula over a class of
intuitionistic models (intuitionistic models with constant domain) iff it is
invariant with respect to asimulations between intuitionistic models
(intuitionistic models with constant domain)
Logical operators for ontological modeling
We show that logic has more to offer to ontologists than standard first order
and modal operators. We first describe some operators of linear logic which we
believe are particularly suitable for ontological modeling, and suggest how to interpret
them within an ontological framework. After showing how they can coexist
with those of classical logic, we analyze three notions of artifact from the literature
to conclude that these linear operators allow for reducing the ontological commitment
needed for their formalization, and even simplify their logical formulation
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