21,606 research outputs found
Learning Linear Temporal Properties
We present two novel algorithms for learning formulas in Linear Temporal
Logic (LTL) from examples. The first learning algorithm reduces the learning
task to a series of satisfiability problems in propositional Boolean logic and
produces a smallest LTL formula (in terms of the number of subformulas) that is
consistent with the given data. Our second learning algorithm, on the other
hand, combines the SAT-based learning algorithm with classical algorithms for
learning decision trees. The result is a learning algorithm that scales to
real-world scenarios with hundreds of examples, but can no longer guarantee to
produce minimal consistent LTL formulas. We compare both learning algorithms
and demonstrate their performance on a wide range of synthetic benchmarks.
Additionally, we illustrate their usefulness on the task of understanding
executions of a leader election protocol
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
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Tools for reformulating logical forms into zero-one mixed integer programs (MIPS)
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Programming (ILP) formulation or a Mixed Integer Programming (MIP) formulation is presented. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. A prototype user interface by which logical forms can be reformulated and the corresponding MIP constructed and analysed within an existing Mathematical Programming modelling system is illustrated. Finally, the steps to formulate a discrete optimisation model in this way are demonstrated by means of an example
The Complexity of Reasoning for Fragments of Autoepistemic Logic
Autoepistemic logic extends propositional logic by the modal operator L. A
formula that is preceded by an L is said to be "believed". The logic was
introduced by Moore 1985 for modeling an ideally rational agent's behavior and
reasoning about his own beliefs. In this paper we analyze all Boolean fragments
of autoepistemic logic with respect to the computational complexity of the
three most common decision problems expansion existence, brave reasoning and
cautious reasoning. As a second contribution we classify the computational
complexity of counting the number of stable expansions of a given knowledge
base. To the best of our knowledge this is the first paper analyzing the
counting problem for autoepistemic logic
On the Complexity of Computing Minimal Unsatisfiable LTL formulas
We show that (1) the Minimal False QCNF search-problem (MF-search) and the
Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE
complete because of the very expressive power of QBF/LTL, (2) we extend the
PSPACE-hardness of the MF decision problem to the MU decision problem. As a
consequence, we deduce a positive answer to the open question of PSPACE
hardness of the inherent Vacuity Checking problem. We even show that the
Inherent Non Vacuous formula search problem is also FPSPACE-complete.Comment: Minimal unsatisfiable cores For LTL causes inherent vacuity checking
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The decision problem of modal product logics with a diagonal, and faulty counter machines
In the propositional modal (and algebraic) treatment of two-variable
first-order logic equality is modelled by a `diagonal' constant, interpreted in
square products of universal frames as the identity (also known as the
`diagonal') relation. Here we study the decision problem of products of two
arbitrary modal logics equipped with such a diagonal. As the presence or
absence of equality in two-variable first-order logic does not influence the
complexity of its satisfiability problem, one might expect that adding a
diagonal to product logics in general is similarly harmless. We show that this
is far from being the case, and there can be quite a big jump in complexity,
even from decidable to the highly undecidable. Our undecidable logics can also
be viewed as new fragments of first- order logic where adding equality changes
a decidable fragment to undecidable. We prove our results by a novel
application of counter machine problems. While our formalism apparently cannot
force reliable counter machine computations directly, the presence of a unique
diagonal in the models makes it possible to encode both lossy and
insertion-error computations, for the same sequence of instructions. We show
that, given such a pair of faulty computations, it is then possible to
reconstruct a reliable run from them
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