364 research outputs found
Analysis of Dialogical Argumentation via Finite State Machines
Dialogical argumentation is an important cognitive activity by which agents
exchange arguments and counterarguments as part of some process such as
discussion, debate, persuasion and negotiation. Whilst numerous formal systems
have been proposed, there is a lack of frameworks for implementing and
evaluating these proposals. First-order executable logic has been proposed as a
general framework for specifying and analysing dialogical argumentation. In
this paper, we investigate how we can implement systems for dialogical
argumentation using propositional executable logic. Our approach is to present
and evaluate an algorithm that generates a finite state machine that reflects a
propositional executable logic specification for a dialogical argumentation
together with an initial state. We also consider how the finite state machines
can be analysed, with the minimax strategy being used as an illustration of the
kinds of empirical analysis that can be undertaken.Comment: 10 page
Dependency Schemes in QBF Calculi: Semantics and Soundness
We study the parametrisation of QBF resolution calculi by dependency schemes. One of the main problems in this area is to understand for which dependency schemes the resulting calculi are sound. Towards this end we propose a semantic framework for variable independence based on âexhibitionâ by QBF models, and use it to express a property of dependency schemes called full exhibition that is known to be sufficient for soundness in Q-resolution. Introducing a generalised form of the long-distance resolution rule, we propose a complete parametrisation of classical long-distance Q-resolution, and show that full exhibition remains sufficient for soundness. We demonstrate that our approach applies to the current research frontiers by proving that the reflexive resolution path dependency scheme is fully exhibited
Understanding Gentzen and Frege Systems for QBF
Recently Beyersdorff, Bonacina, and Chew [10] introduced a natural class of Frege systems for quantified Boolean formulas (QBF) and showed strong lower bounds for restricted versions of these systems. Here we provide a comprehensive analysis of the new extended Frege system from [10], denoted EF + âred, which is a natural extension of classical extended Frege EF. Our main results are the following: Firstly, we prove that the standard Gentzen-style system G*1 p-simulates EF + âred and that G*1 is strictly stronger under standard complexity-theoretic hardness assumptions.
Secondly, we show a correspondence of EF + âred to bounded arithmetic: EF + âred can be seen as the non-uniform propositional version of intuitionistic S12. Specifically, intuitionistic S12 proofs of arbitrary statements in prenex form translate to polynomial-size EF + âred proofs, and EF + âred is in a sense the weakest system with this property. Finally, we show that unconditional lower bounds for EF + âred would imply either a major breakthrough in circuit complexity or in classical proof complexity, and in fact the converse implications hold as well. Therefore, the system EF + âred naturally unites the central problems from circuit and proof complexity.
Technically, our results rest on a formalised strategy extraction theorem for EF + âred akin to witnessing in intuitionistic S12 and a normal form for EF + âred proofs
Evaluating QBF Solvers: Quantifier Alternations Matter
We present an experimental study of the effects of quantifier alternations on
the evaluation of quantified Boolean formula (QBF) solvers. The number of
quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is
directly related to the theoretical hardness of the respective QBF
satisfiability problem in the polynomial hierarchy. We show empirically that
the performance of solvers based on different solving paradigms substantially
varies depending on the numbers of alternations in PCNFs. In related
theoretical work, quantifier alternations have become the focus of
understanding the strengths and weaknesses of various QBF proof systems
implemented in solvers. Our results motivate the development of methods to
evaluate orthogonal solving paradigms by taking quantifier alternations into
account. This is necessary to showcase the broad range of existing QBF solving
paradigms for practical QBF applications. Moreover, we highlight the potential
of combining different approaches and QBF proof systems in solvers.Comment: preprint of a paper to be published at CP 2018, LNCS, Springer,
including appendi
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
We present the latest major release version 6.0 of the quantified Boolean
formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of
the conflict-driven clause learning (CDCL) paradigm implemented in state of the
art propositional satisfiability (SAT) solvers. The Q-resolution calculus
(QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce
QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of
the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0
implements a variant of QCDCL which is based on a generalization of QRES. This
generalization is due to a set of additional axioms and leaves the original
Q-resolution rules unchanged. The generalization of QRES enables QCDCL to
potentially produce exponentially shorter proofs than the traditional variant.
We present an overview of the features implemented in DepQBF and report on
experimental results which demonstrate the effectiveness of generalized QRES in
QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS,
Springer, 201
Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API
We consider the incremental computation of minimal unsatisfiable cores (MUCs)
of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a
novel API to allow for incremental solving based on clause groups. A clause
group is a set of clauses which is incrementally added to or removed from a
previously solved QBF. Our implementation of the novel API is related to
incremental SAT solving based on selector variables and assumptions. However,
the API entirely hides selector variables and assumptions from the user, which
facilitates the integration of DepQBF in other tools. We present implementation
details and, for the first time, report on experiments related to the
computation of MUCs of QBFs using DepQBF's novel clause group API.Comment: (fixed typo), camera-ready version, 6-page tool paper, to appear in
proceedings of SAT 2015, LNCS, Springe
Building Strategies into QBF Proofs
Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution. The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus. Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving
Rescue of Progeria in Trichothiodystrophy by Homozygous Lethal Xpd Alleles
Although compound heterozygosity, or the presence of two different mutant alleles of the same gene, is common in human recessive disease, its potential to impact disease outcome has not been well documented. This is most likely because of the inherent difficulty in distinguishing specific biallelic effects from differences in environment or genetic background. We addressed the potential of different recessive alleles to contribute to the enigmatic pleiotropy associated with XPD recessive disorders in compound heterozygous mouse models. Alterations in this essential helicase, with functions in both DNA repair and basal transcription, result in diverse pathologies ranging from elevated UV sensitivity and cancer predisposition to accelerated segmental progeria. We report a variety of biallelic effects on organismal phenotype attributable to combinations of recessive Xpd alleles, including the following: (i) the ability of homozygous lethal Xpd alleles to ameliorate a variety of disease symptoms when their essential basal transcription function is supplied by a different disease-causing allele, (ii) differential developmental and tissue-specific functions of distinct Xpd allele products, and (iii) interallelic complementation, a phenomenon rarely reported at clinically relevant loci in mammals. Our data suggest a re-evaluation of the contribution of ânullâ alleles to XPD disorders and highlight the potential of combinations of recessive alleles to affect both normal and pathological phenotypic plasticity in mammals
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