6,140 research outputs found
Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription
Circumscription is a representative example of a nonmonotonic reasoning
inference technique. Circumscription has often been studied for first order
theories, but its propositional version has also been the subject of extensive
research, having been shown equivalent to extended closed world assumption
(ECWA). Moreover, entailment in propositional circumscription is a well-known
example of a decision problem in the second level of the polynomial hierarchy.
This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for
entailment in propositional circumscription that explores the relationship of
propositional circumscription to minimal models. The new algorithm is inspired
by ideas commonly used in SAT-based model checking, namely counterexample
guided abstraction refinement. In addition, the new algorithm is refined to
compute the theory closure for generalized close world assumption (GCWA).
Experimental results show that the new algorithm can solve problem instances
that other solutions are unable to solve
Linear-time algorithms for testing the satisfiability of propositional horn formulae
AbstractNew algorithms for deciding whether a (propositional) Horn formula is satisfiable are presented. If the Horn formula A contains K distinct propositional letters and if it is assumed that they are exactly P1,…, PK, the two algorithms presented in this paper run in time O(N), where N is the total number of occurrences of literals in A. By representing a Horn proposition as a graph, the satisfiability problem can be formulated as a data flow problem, a certain type of pebbling. The difference between the two algorithms presented here is the strategy used for pebbling the graph. The first algorithm is based on the principle used for finding the set of nonterminals of a context-free grammar from which the empty string can be derived. The second algorithm is a graph traversal and uses a “call-by-need” strategy. This algorithm uses an attribute grammar to translate a propositional Horn formula to its corresponding graph in linear time. Our formulation of the satisfiability problem as a data flow problem appears to be new and suggests the possibility of improving efficiency using parallel processors
Modal Logics with Hard Diamond-free Fragments
We investigate the complexity of modal satisfiability for certain
combinations of modal logics. In particular we examine four examples of
multimodal logics with dependencies and demonstrate that even if we restrict
our inputs to diamond-free formulas (in negation normal form), these logics
still have a high complexity. This result illustrates that having D as one or
more of the combined logics, as well as the interdependencies among logics can
be important sources of complexity even in the absence of diamonds and even
when at the same time in our formulas we allow only one propositional variable.
We then further investigate and characterize the complexity of the
diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers'
comments. Accepted at LFCS 201
SAT-based Explicit LTL Reasoning
We present here a new explicit reasoning framework for linear temporal logic
(LTL), which is built on top of propositional satisfiability (SAT) solving. As
a proof-of-concept of this framework, we describe a new LTL satisfiability
tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the
effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly
outperforms all existing LTL satisfiability solvers. Furthermore, we show that
the framework can be extended from propositional LTL to assertional LTL (where
we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and
demonstrating that this can yield an exponential improvement in performance
Model-Checking Problems as a Basis for Parameterized Intractability
Most parameterized complexity classes are defined in terms of a parameterized
version of the Boolean satisfiability problem (the so-called weighted
satisfiability problem). For example, Downey and Fellow's W-hierarchy is of
this form. But there are also classes, for example, the A-hierarchy, that are
more naturally characterised in terms of model-checking problems for certain
fragments of first-order logic.
Downey, Fellows, and Regan were the first to establish a connection between
the two formalisms by giving a characterisation of the W-hierarchy in terms of
first-order model-checking problems. We improve their result and then prove a
similar correspondence between weighted satisfiability and model-checking
problems for the A-hierarchy and the W^*-hierarchy. Thus we obtain very uniform
characterisations of many of the most important parameterized complexity
classes in both formalisms.
Our results can be used to give new, simple proofs of some of the core
results of structural parameterized complexity theory.Comment: Changes in since v2: Metadata update
On Sub-Propositional Fragments of Modal Logic
In this paper, we consider the well-known modal logics ,
, , and , and we study some of their
sub-propositional fragments, namely the classical Horn fragment, the Krom
fragment, the so-called core fragment, defined as the intersection of the Horn
and the Krom fragments, plus their sub-fragments obtained by limiting the use
of boxes and diamonds in clauses. We focus, first, on the relative expressive
power of such languages: we introduce a suitable measure of expressive power,
and we obtain a complex hierarchy that encompasses all fragments of the
considered logics. Then, after observing the low expressive power, in
particular, of the Horn fragments without diamonds, we study the computational
complexity of their satisfiability problem, proving that, in general, it
becomes polynomial
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