4,257 research outputs found
LangPro: Natural Language Theorem Prover
LangPro is an automated theorem prover for natural language
(https://github.com/kovvalsky/LangPro). Given a set of premises and a
hypothesis, it is able to prove semantic relations between them. The prover is
based on a version of analytic tableau method specially designed for natural
logic. The proof procedure operates on logical forms that preserve linguistic
expressions to a large extent. %This property makes the logical forms easily
obtainable from syntactic trees. %, in particular, Combinatory Categorial
Grammar derivation trees. The nature of proofs is deductive and transparent. On
the FraCaS and SICK textual entailment datasets, the prover achieves high
results comparable to state-of-the-art.Comment: 6 pages, 8 figures, Conference on Empirical Methods in Natural
Language Processing (EMNLP) 201
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
Reductions of Young tableau bijections
We introduce notions of linear reduction and linear equivalence of bijections
for the purposes of study bijections between Young tableaux. Originating in
Theoretical Computer Science, these notions allow us to give a unified view of
a number of classical bijections, and establish formal connections between
them.Comment: 42 pages, 15 figure
Tableaux for Policy Synthesis for MDPs with PCTL* Constraints
Markov decision processes (MDPs) are the standard formalism for modelling
sequential decision making in stochastic environments. Policy synthesis
addresses the problem of how to control or limit the decisions an agent makes
so that a given specification is met. In this paper we consider PCTL*, the
probabilistic counterpart of CTL*, as the specification language. Because in
general the policy synthesis problem for PCTL* is undecidable, we restrict to
policies whose execution history memory is finitely bounded a priori.
Surprisingly, no algorithm for policy synthesis for this natural and
expressive framework has been developed so far. We close this gap and describe
a tableau-based algorithm that, given an MDP and a PCTL* specification, derives
in a non-deterministic way a system of (possibly nonlinear) equalities and
inequalities. The solutions of this system, if any, describe the desired
(stochastic) policies.
Our main result in this paper is the correctness of our method, i.e.,
soundness, completeness and termination.Comment: This is a long version of a conference paper published at TABLEAUX
2017. It contains proofs of the main results and fixes a bug. See the
footnote on page 1 for detail
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