ExpTime Tableaux for Using Sound Global Caching

Goré, Rajeev; Nguyen, Linh Anh

doi:10.1007/s10817-011-9243-0

Cited by 23 publications

(55 citation statements)

References 31 publications

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“…First, this algorithm helps us reduce a DL-based problem to a SAT based problem so that we can delegate efficient reasoning by using proven to be efficient algorithms. The other reason is that we simplified the pre-model structure from an AND-OR graph [6] to an AND-only graph, i.e., all nodes in the discourse have to be satisfiable to make the corresponding TBox satisfiable. The "OR" portion in the graph with its reasoning algorithm is completely merged to the "AND" node.…”

Section: Resultsmentioning

confidence: 99%

“…Solutions to fix the unsoundness are discussed in [3,6]. The solution introduced in [6] is widely considered to be the best so far.…”

Section: Integrating Learning Into Reasoningmentioning

confidence: 99%

“…Solutions to fix the unsoundness are discussed in [3,6]. The solution introduced in [6] is widely considered to be the best so far. However, it requires EXPSpace in the worst case to construct a pre-model which can easily cause the reasoning algorithm to become intractable.…”

Section: Integrating Learning Into Reasoningmentioning

confidence: 99%

“…The research on EXPTime Tableau for ALC [4] (by applying global caching) has been further developed and implemented by [6,7]. These kinds of algorithms either heavily use subset checking or require EXPSpace to construct the pre-model.…”

Section: Related Workmentioning

confidence: 99%

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Intelligent Tableau Algorithm for DL Reasoning

Zuo

Haarslev

2013

Lecture Notes in Computer Science

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Abstract. Although state-of-the-art description logic (DL) reasoners are equipped with a comprehensive set of optimizations, reasoning performance is still a major bottleneck in both research and real world applications. In this paper, we propose a sound and complete algorithm called the intelligent tableau algorithm by incorporating comprehensive learning techniques to tackle all DL reasoning tasks. We also provide a reference implementation reasoner called LIGHT for the DL ALC dialect based on the algorithm we developed. Preliminary tests indicate that significant improvements can be achieved, i.e., compared to other state-of-the-art reasoners, LIGHT is up to two orders of magnitude faster for simple problems and several orders of magnitude faster for more difficult problems. Even though in this work our discussion is restricted to the ALC reasoning problem, our conjecture is that the algorithm developed can easily be extended to super-logics of ALC.

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Section: Resultsmentioning

confidence: 99%

“…Solutions to fix the unsoundness are discussed in [3,6]. The solution introduced in [6] is widely considered to be the best so far.…”

Section: Integrating Learning Into Reasoningmentioning

confidence: 99%

Section: Integrating Learning Into Reasoningmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Intelligent Tableau Algorithm for DL Reasoning

Zuo

Haarslev

2013

Lecture Notes in Computer Science

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“…Although optimal tableau algorithms that avoid this behaviour are known [6], they are rarely used by practitioners because they are difficult to implement [1]. Recently, it has been shown that both optimality and ease of implementation can be reconciled while keeping the feasibility of tableaubased algorithms for the description logics ALC and ALCI [10,13] by employing so-called "global caching". The resulting tableau algorithms explore a graph of nodes, rather than a tree with distinct branches, since subsequent incarnations of a node lead to a "cache hit" to the first incarnation on a previous branch.…”

Section: Introductionmentioning

confidence: 99%

Optimal Tableau Algorithms for Coalgebraic Logics

Goré

Kupke

Pattinson

2010

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Deciding whether a modal formula is satisfiable with respect to a given set of (global) assumptions is a question of fundamental importance in applications of logic in computer science. Tableau methods have proved extremely versatile for solving this problem for many different individual logics but they typically do not meet the known complexity bounds for the logics in question. Recently, it has been shown that optimality can be obtained for some logics while retaining practicality by using a technique called "global caching". Here, we show that global caching is applicable to all logics that can be equipped with coalgebraic semantics, for example, classical modal logic, graded modal logic, probabilistic modal logic and coalition logic. In particular, the coalgebraic approach also covers logics that combine these various features. We thus show that global caching is a widely applicable technique and also provide foundations for optimal tableau algorithms that uniformly apply to a large class of modal logics.

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Optimal Satisfiability Checking for Arithmetic $$\mu $$-Calculi

Hausmann

Schröder

2019

Lecture Notes in Computer Science

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The coalgebraic µ-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic µ-calculus includes an exponential time upper bound on satisfiability checking, which however requires a well-behaved set of tableau rules for the next-step modalities. Such rules are not available in all cases of interest, in particular ones involving either integer weights as in the graded µ-calculus, or real-valued weights in combination with non-linear arithmetic. In the present paper, we prove the same upper complexity bound under more general assumptions, specifically regarding the complexity of the (much simpler) satisfiability problem for the underlying so-called one-step logic, roughly described as the nesting-free next-step fragment of the logic. We also present a generic global caching algorithm that is suitable for practical use and supports on-the-fly satisfiability checking. Example applications include new exponential-time upper bounds for satisfiability checking in an extension of the graded µcalculus with Presburger arithmetic, as well as an extension of the (twovalued) probabilistic µ-calculus with polynomial inequalities. As a side result, we moreover obtain a new upper bound O(((nk)!) 2 ) on minimum model size for satisfiable formulas for all coalgebraic µ-calculi, where n is the size of the formula and k its alternation depth.

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ExpTime Tableaux for Using Sound Global Caching

Cited by 23 publications

References 31 publications

Intelligent Tableau Algorithm for DL Reasoning

Intelligent Tableau Algorithm for DL Reasoning

Optimal Tableau Algorithms for Coalgebraic Logics

Optimal Satisfiability Checking for Arithmetic $$\mu $$-Calculi

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