18,683 research outputs found
An Observation Concerning Porte’s Rule in Modal Logic
It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ◊A, or else no consistent normal modal logic contains ◊¬A
Ecumenical modal logic
The discussion about how to put together Gentzen's systems for classical and
intuitionistic logic in a single unified system is back in fashion. Indeed,
recently Prawitz and others have been discussing the so called Ecumenical
Systems, where connectives from these logics can co-exist in peace. In Prawitz'
system, the classical logician and the intuitionistic logician would share the
universal quantifier, conjunction, negation, and the constant for the absurd,
but they would each have their own existential quantifier, disjunction, and
implication, with different meanings. Prawitz' main idea is that these
different meanings are given by a semantical framework that can be accepted by
both parties. In a recent work, Ecumenical sequent calculi and a nested system
were presented, and some very interesting proof theoretical properties of the
systems were established. In this work we extend Prawitz' Ecumenical idea to
alethic K-modalities
Non normal logics: semantic analysis and proof theory
We introduce proper display calculi for basic monotonic modal logic,the
conditional logic CK and a number of their axiomatic extensions. These calculi
are sound, complete, conservative and enjoy cut elimination and subformula
property. Our proposal applies the multi-type methodology in the design of
display calculi, starting from a semantic analysis based on the translation
from monotonic modal logic to normal bi-modal logic
Refinement Modal Logic
In this paper we present {\em refinement modal logic}. A refinement is like a
bisimulation, except that from the three relational requirements only `atoms'
and `back' need to be satisfied. Our logic contains a new operator 'all' in
addition to the standard modalities 'box' for each agent. The operator 'all'
acts as a quantifier over the set of all refinements of a given model. As a
variation on a bisimulation quantifier, this refinement operator or refinement
quantifier 'all' can be seen as quantifying over a variable not occurring in
the formula bound by it. The logic combines the simplicity of multi-agent modal
logic with some powers of monadic second-order quantification. We present a
sound and complete axiomatization of multi-agent refinement modal logic. We
also present an extension of the logic to the modal mu-calculus, and an
axiomatization for the single-agent version of this logic. Examples and
applications are also discussed: to software verification and design (the set
of agents can also be seen as a set of actions), and to dynamic epistemic
logic. We further give detailed results on the complexity of satisfiability,
and on succinctness
The Expressive Power of Modal Dependence Logic
We study the expressive power of various modal logics with team semantics. We
show that exactly the properties of teams that are downward closed and closed
under team k-bisimulation, for some finite k, are definable in modal logic
extended with intuitionistic disjunction. Furthermore, we show that the
expressive power of modal logic with intuitionistic disjunction and extended
modal dependence logic coincide. Finally we establish that any translation from
extended modal dependence logic into modal logic with intuitionistic
disjunction increases the size of some formulas exponentially.Comment: 19 page
To Teach Modal Logic: An Opinionated Survey
I aim to promote an alternative agenda for teaching modal logic chiefly
inspired by the relationships between modal logic and philosophy. The guiding
idea for this proposal is a reappraisal of the interest of modal logic in
philosophy, which do not stem mainly from mathematical issues, but which is
motivated by central problems of philosophy and language. I will point out some
themes to start elaborating a guide for a more comprehensive approach to teach
modal logic, and consider the contributions of dual-process theories in
cognitive science, in order to explore a pedagogical framework for the proposed
point of view.Comment: Proceedings of the Fourth International Conference on Tools for
Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M.
Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat,
Fran\c{c}ois Schwarzentrube
Coherence in Modal Logic
A variety is said to be coherent if the finitely generated subalgebras of its
finitely presented members are also finitely presented. In a recent paper by
the authors it was shown that coherence forms a key ingredient of the uniform
deductive interpolation property for equational consequence in a variety, and a
general criterion was given for the failure of coherence (and hence uniform
deductive interpolation) in varieties of algebras with a term-definable
semilattice reduct. In this paper, a more general criterion is obtained and
used to prove the failure of coherence and uniform deductive interpolation for
a broad family of modal logics, including K, KT, K4, and S4
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