145,919 research outputs found
Complexity Results for Modal Dependence Logic
Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances
the basic modal language by an operator =(). For propositional variables
p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is
determined by those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation,
2009) showed that satisfiability for modal dependence logic is complete for
nondeterministic exponential time. In this paper we consider fragments of modal
dependence logic obtained by restricting the set of allowed propositional
connectives. We show that satisfibility for poor man's dependence logic, the
language consisting of formulas built from literals and dependence atoms using
conjunction, necessity and possibility (i.e., disallowing disjunction), remains
NEXPTIME-complete. If we only allow monotone formulas (without negation, but
with disjunction), the complexity drops to PSPACE-completeness. We also extend
V\"a\"an\"anen's language by allowing classical disjunction besides dependence
disjunction and show that the satisfiability problem remains NEXPTIME-complete.
If we then disallow both negation and dependence disjunction, satistiability is
complete for the second level of the polynomial hierarchy. In this way we
completely classify the computational complexity of the satisfiability problem
for all restrictions of propositional and dependence operators considered by
V\"a\"an\"anen and Sevenster.Comment: 22 pages, full version of CSL 2010 pape
Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic
In this paper, we initiate a systematic study of the parametrised complexity
in the field of Dependence Logics which finds its origin in the Dependence
Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this
logic (PDL) and investigate a variety of parametrisations with respect to the
central decision problems. The model checking problem (MC) of PDL is
NP-complete. The subject of this research is to identify a list of
parametrisations (formula-size, treewidth, treedepth, team-size, number of
variables) under which MC becomes fixed-parameter tractable. Furthermore, we
show that the number of disjunctions or the arity of dependence atoms
(dep-arity) as a parameter both yield a paraNP-completeness result. Then, we
consider the satisfiability problem (SAT) showing a different picture: under
team-size, or dep-arity SAT is paraNP-complete whereas under all other
mentioned parameters the problem is in FPT. Finally, we introduce a variant of
the satisfiability problem, asking for teams of a given size, and show for this
problem an almost complete picture.Comment: Update includes refined result
Decidability of predicate logics with team semantics
We study the complexity of predicate logics based on team semantics. We show
that the satisfiability problems of two-variable independence logic and
inclusion logic are both NEXPTIME-complete. Furthermore, we show that the
validity problem of two-variable dependence logic is undecidable, thereby
solving an open problem from the team semantics literature. We also briefly
analyse the complexity of the Bernays-Sch\"onfinkel-Ramsey prefix classes of
dependence logic.Comment: Extended version of a MFCS 2016 article. Changes on the earlier arXiv
version: title changed, added the result on validity of two-variable
dependence logic, restructurin
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
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
Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension
Dependence is an important concept for many tasks in artificial intelligence.
A task can be executed more efficiently by discarding something independent
from the task. In this paper, we propose two novel notions of dependence in
propositional logic: formula-formula dependence and formula forgetting. The
first is a relation between formulas capturing whether a formula depends on
another one, while the second is an operation that returns the strongest
consequence independent of a formula. We also apply these two notions in two
well-known issues: belief update and conservative extension. Firstly, we define
a new update operator based on formula-formula dependence. Furthermore, we
reduce conservative extension to formula forgetting.Comment: We find a mistake in this version and we need a period of time to fix
i
A Fragment of Dependence Logic Capturing Polynomial Time
In this paper we study the expressive power of Horn-formulae in dependence
logic and show that they can express NP-complete problems. Therefore we define
an even smaller fragment D-Horn* and show that over finite successor structures
it captures the complexity class P of all sets decidable in polynomial time.
Furthermore we study the question which of our results can ge generalized to
the case of open formulae of D-Horn* and so-called downwards monotone
polynomial time properties of teams
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