Cool – A Generic Reasoner for Coalgebraic Hybrid Logics (System Description)

Gorín, Daniel; Pattinson, Dirk; Schröder, Lutz; Widmann, Florian; Wißmann, Thorsten

doi:10.1007/978-3-319-08587-6_31

Cited by 10 publications

(5 citation statements)

References 17 publications

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“…We have implemented the permutation satisfiability games as an extension of the Coalgebraic Ontology Logic Reasoner (COOL) [11], a generic reasoner for coalgebraic modal logics 1 . COOL achieves its genericity by instantiating an abstract reasoner that works for all coalgebraic logics to concrete instances of logics.…”

Section: Implementation and Benchmarkingmentioning

confidence: 99%

“…The resulting decision procedure generalizes to the weakly aconjunctive coalgebraic μ-calculus, thus covering also, e.g., probabilistic and alternatingtime versions of the μ-calculus. The generic algorithm has been implemented as an extension of the Coalgebraic Ontology Logic Reasoner (COOL) [11,13]. Our implementation constructs and solves the presented permutation games onthe-fly, possibly finishing satisfiability proofs early, and shows promising initial results.…”

Section: Introductionmentioning

confidence: 99%

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Permutation Games for the Weakly Aconjunctive $$\mu $$ μ -Calculus

Hausmann

Schröder

Deifel

2018

Tools and Algorithms for the Construction and Analysis of Systems

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We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the μ-calculus. To this end we devise a method that determinizes limit-deterministic parity automata of size n with k priorities through limit-deterministic Büchi automata to deterministic parity automata of size O((nk)!) and with O(nk) priorities. The construction relies on limit-determinism to avoid the full complexity of the Safra/Pitermanconstruction by using partial permutations of states in place of Safra-Trees. By showing that limit-deterministic parity automata can be used to recognize unsuccessful branches in pre-tableaux for the weakly aconjunctive μ-calculus, we obtain satisfiability games of size O((nk)!) with O(nk) priorities for weakly aconjunctive input formulas of size n and alternation-depth k. A prototypical implementation that employs a tableau-based global caching algorithm to solve these games on-the-fly shows promising initial results.

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Section: Implementation and Benchmarkingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Permutation Games for the Weakly Aconjunctive $$\mu $$ μ -Calculus

Hausmann

Schröder

Deifel

2018

Tools and Algorithms for the Construction and Analysis of Systems

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“…The global caching algorithm has been implemented as an extension of the Coalgebraic Ontology Logic Reasoner (COOL) [21], a generic reasoner for coalgebraic modal logics, available at https://www8.cs.fau.de/research:software:cool. COOL achieves its genericity by instantiating an abstract core reasoner that works for all coalgebraic logics to concrete instances of logics; our global caching algorithm extends this core.…”

Section: Implementation and Benchmarkingmentioning

confidence: 99%

Global Caching for the Flat Coalgebraic µ-Calculus

Hausmann

Schröder

2015

2015 22nd International Symposium on Temporal Representation and Reasoning (TIME)

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We present a sound, complete, and optimal single-pass tableau algorithm for the alternation-free µ-calculus. The algorithm supports global caching with intermediate propagation and runs in time 2 O(n) . In game-theoretic terms, our algorithm integrates the steps for constructing and solving the Büchi game arising from the input tableau into a single procedure; this is done onthe-fly, i.e. may terminate before the game has been fully constructed. This suggests a slogan to the effect that global caching = game solving on-the-fly. A prototypical implementation shows promising initial results.Parikh's game logic [31], or probabilistic fixpoint logic. To aid readability, we phrase our results in terms of the relational µ-calculus, and discuss the coalgebraic generalization only at the end of Section 4. The model construction in the completeness proof yields models of size 2 O(n) .We have implemented of our algorithm as an extension of the Coalgebraic Ontology Logic Reasoner COOL, a generic reasoner for coalgebraic modal logics [21]; given the current state of the implementation of instance logics in COOL, this means that we effectively support alternation-free fragments of relational, monotone, and alternating-time [1] µ-calculi, thus in particular covering CTL and ATL. We have evaluated the tool in comparison with existing reasoners on benchmark formulas for CTL [18] (which appears to be the only candidate logic for which well-developed benchmarks are currently available) and on random formulas for ATL and the alternation-free relational µ-calculus, with promising results; details are discussed in Section 5. Related WorkThe theoretical upper bound ExpTime has been established for the full coalgebraic µ-calculus [5] (and earlier for instances such as the alternating-time µ-calculus AMC [35]), using a multi-pass algorithm that combines games and automata in a similar way as for the standard relational case, in particular involving the Safra construction. Global caching has been employed successfully for a variety of description logics [17, 20], and lifted to the level of generality of coalgebraic logics with global assumptions [15] and nominals [16].A tableaux-based non-optimal (NExpTime) decision procedure for the full µ-calculus has been proposed in [23]. Friedmann and Lange [12] describe an optimal tableau method for the full µ-calculus that, unlike most other methods including the one we present here, makes do without requiring guardedness. Like earlier algorithms for the full µ-calculus, the algorithm constructs and solves a parity game, and in principle allows for an on-thefly implementation. The models constructed in the completeness proof are asymptotically larger than ours, but presumably the proof can be adapted for the alternation-free case by using determinization of co-Büchi automata [28] instead of Safra's determinization of Büchi automata [34] to yield models of size 2 O(n) , like ours. For non-relational instances of the coalgebraic µ-calculus, including the alternation-free fragment of the alternatin...

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“…The above-mentioned logical patterns are thus essentially formulae in coalgebraic logic with placeholders for subformulae. Reasoning support is provided, either off-the-shelf or by easy implementation of further instance logics, via the generic Coalgebraic Ontology Logic (COOL) reasoner [12]. An important desideratum for further research is to provide support for similarity reasoning (e.g.…”

Section: Coalgebraic Logicmentioning

confidence: 99%

Reconstructing Arguments from Noisy Text

et al. 2020

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Social media are of paramount importance to public discourse. RANT aims to contribute methods and formalisms for extracting, representing, and processing arguments from noisy text found in social media discussions, using a large corpus of pre-referendum Brexit tweets as a running case study. We identify recurring linguistic argumentation patterns in a corpus-linguistic analysis and formulate corresponding corpus queries to extract arguments automatically. Given the huge amount of social media data available, our approach aims at high precision at the possible price of low recall. Argumentation patterns are directly associated with logical patterns in a dedicated formalism and accordingly, individual arguments are directly parsed as logical formulae. The logical formalism for argument representation features a broad range of modalities capturing real-life modes of expression. We cast this formalism as a family of instance logics in the generic framework of coalgebraic logic and complement it by a flexible framework to represent relationships between arguments; including standard relations like attack and support but also relations extracted from metadata. Some relations are inferred from the logical content of individual arguments. We are in the process of developing suitable generalizations of various extension semantics for argumentation frameworks combined with corresponding algorithmic methods to allow for the automated retrieval of large-scale argumentative positions. The work is supported by the DFG under Project 377333057 "Reconstructing Arguments from Noisy Text (RANT)".

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Cool – A Generic Reasoner for Coalgebraic Hybrid Logics (System Description)

Cited by 10 publications

References 17 publications

Permutation Games for the Weakly Aconjunctive $$\mu $$ μ -Calculus

Permutation Games for the Weakly Aconjunctive $$\mu $$ μ -Calculus

Global Caching for the Flat Coalgebraic µ-Calculus

Reconstructing Arguments from Noisy Text

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