22 research outputs found
Minimal Proof Search for Modal Logic K Model Checking
Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K.
While the model checking problems for LTL and to a lesser extent ATL have been
very active research areas for the past decades, the model checking problem for
the more basic Multi-agent Modal Logic K (MMLK) has important applications as a
formal framework for perfect information multi-player games on its own.
We present Minimal Proof Search (MPS), an effort number based algorithm
solving the model checking problem for MMLK. We prove two important properties
for MPS beyond its correctness. The (dis)proof exhibited by MPS is of minimal
cost for a general definition of cost, and MPS is an optimal algorithm for
finding (dis)proofs of minimal cost. Optimality means that any comparable
algorithm either needs to explore a bigger or equal state space than MPS, or is
not guaranteed to find a (dis)proof of minimal cost on every input.
As such, our work relates to A* and AO* in heuristic search, to Proof Number
Search and DFPN+ in two-player games, and to counterexample minimization in
software model checking.Comment: Extended version of the JELIA 2012 paper with the same titl
Context-Free Path Queries on RDF Graphs
Navigational graph queries are an important class of queries that canextract
implicit binary relations over the nodes of input graphs. Most of the
navigational query languages used in the RDF community, e.g. property paths in
W3C SPARQL 1.1 and nested regular expressions in nSPARQL, are based on the
regular expressions. It is known that regular expressions have limited
expressivity; for instance, some natural queries, like same generation-queries,
are not expressible with regular expressions. To overcome this limitation, in
this paper, we present cfSPARQL, an extension of SPARQL query language equipped
with context-free grammars. The cfSPARQL language is strictly more expressive
than property paths and nested expressions. The additional expressivity can be
used for modelling graph similarities, graph summarization and ontology
alignment. Despite the increasing expressivity, we show that cfSPARQL still
enjoys a low computational complexity and can be evaluated efficiently.Comment: 25 page
Verifying context-sensitive treebanks and heuristic parses in polynomial time
Proceedings of the 17th Nordic Conference of Computational Linguistics
NODALIDA 2009.
Editors: Kristiina Jokinen and Eckhard Bick.
NEALT Proceedings Series, Vol. 4 (2009), 190-197.
© 2009 The editors and contributors.
Published by
Northern European Association for Language
Technology (NEALT)
http://omilia.uio.no/nealt .
Electronically published at
Tartu University Library (Estonia)
http://hdl.handle.net/10062/9206
FO = FO^3 for Linear Orders with Monotone Binary Relations
We show that over the class of linear orders with additional binary relations satisfying some monotonicity conditions, monadic first-order logic has the three-variable property. This generalizes (and gives a new proof of) several known results, including the fact that monadic first-order logic has the three-variable property over linear orders, as well as over (R,<,+1), and answers some open questions mentioned in a paper from Antonopoulos, Hunter, Raza and Worrell [FoSSaCS 2015]. Our proof is based on a translation of monadic first-order logic formulas into formulas of a star-free variant of Propositional Dynamic Logic, which are in turn easily expressible in monadic first-order logic with three variables
Model Checking Parse Trees
Parse trees are fundamental syntactic structures in both computational
linguistics and compilers construction. We argue in this paper that, in both
fields, there are good incentives for model-checking sets of parse trees for
some word according to a context-free grammar. We put forward the adequacy of
propositional dynamic logic (PDL) on trees in these applications, and study as
a sanity check the complexity of the corresponding model-checking problem:
although complete for exponential time in the general case, we find natural
restrictions on grammars for our applications and establish complexities
ranging from nondeterministic polynomial time to polynomial space in the
relevant cases.Comment: 21 + x page
Model Checking Timed Recursive CTL
We introduce Timed Recursive CTL, a merger of two extensions of the well-known branching-time logic CTL: Timed CTL is interpreted over real-time systems like timed automata; Recursive CTL introduces a powerful recursion operator which takes the expressiveness of this logic CTL well beyond that of regular properties. The result is an expressive logic for real-time properties. We show that its model checking problem is decidable over timed automata, namely 2-EXPTIME-complete
PDL as a Multi-Agent Strategy Logic
Propositional Dynamic Logic or PDL was invented as a logic for reasoning
about regular programming constructs. We propose a new perspective on PDL as a
multi-agent strategic logic (MASL). This logic for strategic reasoning has
group strategies as first class citizens, and brings game logic closer to
standard modal logic. We demonstrate that MASL can express key notions of game
theory, social choice theory and voting theory in a natural way, we give a
sound and complete proof system for MASL, and we show that MASL encodes
coalition logic. Next, we extend the language to epistemic multi-agent
strategic logic (EMASL), we give examples of what it can express, we propose to
use it for posing new questions in epistemic social choice theory, and we give
a calculus for reasoning about a natural class of epistemic game models. We end
by listing avenues for future research and by tracing connections to a number
of other logics for reasoning about strategies.Comment: 10 pages, Poster presentation at TARK 2013 (arXiv:1310.6382)
http://www.tark.or