182,580 research outputs found
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
lim+, delta+, and Non-Permutability of beta-Steps
Using a human-oriented formal example proof of the (lim+) theorem, i.e. that
the sum of limits is the limit of the sum, which is of value for reference on
its own, we exhibit a non-permutability of beta-steps and delta+-steps
(according to Smullyan's classification), which is not visible with
non-liberalized delta-rules and not serious with further liberalized
delta-rules, such as the delta++-rule. Besides a careful presentation of the
search for a proof of (lim+) with several pedagogical intentions, the main
subject is to explain why the order of beta-steps plays such a practically
important role in some calculi.Comment: ii + 36 page
Searching for a Solution to Program Verification=Equation Solving in CCS
International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides âagent-specificâ results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model
Cooperation between Top-Down and Bottom-Up Theorem Provers
Top-down and bottom-up theorem proving approaches each have specific
advantages and disadvantages. Bottom-up provers profit from strong redundancy
control but suffer from the lack of goal-orientation, whereas top-down provers
are goal-oriented but often have weak calculi when their proof lengths are
considered. In order to integrate both approaches, we try to achieve
cooperation between a top-down and a bottom-up prover in two different ways:
The first technique aims at supporting a bottom-up with a top-down prover. A
top-down prover generates subgoal clauses, they are then processed by a
bottom-up prover. The second technique deals with the use of bottom-up
generated lemmas in a top-down prover. We apply our concept to the areas of
model elimination and superposition. We discuss the ability of our techniques
to shorten proofs as well as to reorder the search space in an appropriate
manner. Furthermore, in order to identify subgoal clauses and lemmas which are
actually relevant for the proof task, we develop methods for a relevancy-based
filtering. Experiments with the provers SETHEO and SPASS performed in the
problem library TPTP reveal the high potential of our cooperation approaches
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