499 research outputs found
Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on
Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200
PSPACE Bounds for Rank-1 Modal Logics
For lack of general algorithmic methods that apply to wide classes of logics,
establishing a complexity bound for a given modal logic is often a laborious
task. The present work is a step towards a general theory of the complexity of
modal logics. Our main result is that all rank-1 logics enjoy a shallow model
property and thus are, under mild assumptions on the format of their
axiomatisation, in PSPACE. This leads to a unified derivation of tight
PSPACE-bounds for a number of logics including K, KD, coalition logic, graded
modal logic, majority logic, and probabilistic modal logic. Our generic
algorithm moreover finds tableau proofs that witness pleasant proof-theoretic
properties including a weak subformula property. This generality is made
possible by a coalgebraic semantics, which conveniently abstracts from the
details of a given model class and thus allows covering a broad range of logics
in a uniform way
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
A Propositional CONEstrip Algorithm
We present a variant of the CONEstrip algorithm for checking whether the origin lies in a finitely generated convex cone that can be open, closed, or neither. This variant is designed to deal efficiently with problems where the rays defining the cone are specified as linear combinations of propositional sentences. The variant differs from the original algorithm in that we apply row generation techniques. The generator problem is WPMaxSAT, an optimization variant of SAT; both can be solved with specialized solvers or integer linear programming techniques. We additionally show how optimization problems over the cone can be solved by using our propositional CONEstrip algorithm as a preprocessor. The algorithm is designed to support consistency and inference computations within the theory of sets of desirable gambles. We also make a link to similar computations in probabilistic logic, conditional probability assessments, and imprecise probability theory
Engineering the development of quantum programs: Application to the Boolean satisfiability problem
The development of quantum programs is becoming a reality due to the rapid advancement of quantum computing. Over the past few years, a multitude of hardware platforms, algorithms, and programming languages have emerged to support this paradigm. By the very nature of Quantum Mechanics principles, there is an enormous change of philosophy when building quantum programs, which operate in a probabilistic space, unlike the deterministic behaviour shown by classical programming languages. These conceptual differences can be overcome by using techniques and tools of Software Engineering. In this paper, we apply Model-Driven Engineering techniques in a systematic way to ease the generation of quantum programs and we apply it to solve the satisfiability problem, very important in many engineering domains like verification of discrete systems and test of integrated circuits. To that aim, we contribute with a metamodel for representing quantum circuits and a model-to-text transformation to generate working IBM Qiskit code. This model-driven infrastructure is employed to automatically generate quantum programs from SAT equations through a model-to-model transformation that embeds Grover’s algorithm. Besides, we provide formulas for calculating the number of required quantum elements from SAT equations, crucial in the current context of limited quantum resources. The interoperability with other tools and the extensibility to target additional quantum platforms is guaranteed thanks to the use of a model-based toolchain. We cover several usage scenarios to validate the approach, providing exemplary SAT equations, the generated Qiskit code and the results of executing this code in IBM Quantum infrastructure.We acknowledge the use of IBM Quantum services for this work. The views expressed in this paper are those of the authors, and do not reflect the official policy or position of IBM or the IBM Quantum team
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