30,121 research outputs found
Complexity of validity for propositional dependence logics
We study the validity problem for propositional dependence logic, modal
dependence logic and extended modal dependence logic. We show that the validity
problem for propositional dependence logic is NEXPTIME-complete. In addition,
we establish that the corresponding problem for modal dependence logic and
extended modal dependence logic is NEXPTIME-hard and in NEXPTIME^NP.Comment: In Proceedings GandALF 2014, arXiv:1408.556
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
Axiomatizing propositional dependence logics
We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and modal logic. In addition, we give novel labeled tableau calculi for PD, MDL, and EMDL. We prove soundness, completeness and termination for each of the labeled calculi
Axiomatizing modal inclusion logic
Modal inclusion logic is modal logic extended with inclusion atoms. It is the modal variant of first-order inclusion logic, which was introduced by Galliani (2012). Inclusion logic is a main variant of dependence logic (Väänänen 2007). Dependence logic and its variants adopt team semantics, introduced by Hodges (1997). Under team semantics, a modal (inclusion) logic formula is evaluated in a set of states, called a team. The inclusion atom is a type of dependency atom, which describes that the possible values a sequence of formulas can obtain are values of another sequence of formulas. In this thesis, we introduce a sound and complete natural deduction system for modal inclusion logic, which is currently missing in the literature.
The thesis consists of an introductory part, in which we recall the definitions and basic properties of modal logic and modal inclusion logic, followed by two main parts. The first part concerns the expressive power of modal inclusion logic. We review the result of Hella and Stumpf (2015) that modal inclusion logic is expressively complete: A class of Kripke models with teams is closed under unions, closed under k-bisimulation for some natural number k, and has the empty team property if and only if the class can be defined with a modal inclusion logic formula. Through the expressive completeness proof, we obtain characteristic formulas for classes with these three properties. This also provides a normal form for formulas in MIL. The proof of this result is due to Hella and Stumpf, and we suggest a simplification to the normal form by making it similar to the normal form introduced by Kontinen et al. (2014).
In the second part, we introduce a sound and complete natural deduction proof system for modal inclusion logic. Our proof system builds on the proof systems defined for modal dependence logic and propositional inclusion logic by Yang (2017, 2022). We show the completeness theorem using the normal form of modal inclusion logic
The expressive power of modal logic with inclusion atoms
Modal inclusion logic is the extension of basic modal logic with inclusion
atoms, and its semantics is defined on Kripke models with teams. A team of a
Kripke model is just a subset of its domain. In this paper we give a complete
characterisation for the expressive power of modal inclusion logic: a class of
Kripke models with teams is definable in modal inclusion logic if and only if
it is closed under k-bisimulation for some integer k, it is closed under
unions, and it has the empty team property. We also prove that the same
expressive power can be obtained by adding a single unary nonemptiness operator
to modal logic. Furthermore, we establish an exponential lower bound for the
size of the translation from modal inclusion logic to modal logic with the
nonemptiness operator.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
A Team Based Variant of CTL
We introduce two variants of computation tree logic CTL based on team
semantics: an asynchronous one and a synchronous one. For both variants we
investigate the computational complexity of the satisfiability as well as the
model checking problem. The satisfiability problem is shown to be
EXPTIME-complete. Here it does not matter which of the two semantics are
considered. For model checking we prove a PSPACE-completeness for the
synchronous case, and show P-completeness for the asynchronous case.
Furthermore we prove several interesting fundamental properties of both
semantics.Comment: TIME 2015 conference version, modified title and motiviatio
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
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