22,049 research outputs found
Encoding argument graphs in logic
International audienceArgument graphs are a common way to model argumentative reasoning. For reasoning or computational purposes, such graphs may have to be encoded in a given logic. This paper aims at providing a systematic approach for this encoding. This approach relies upon a general, principle-based characterization of argumentation semantics
Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus
The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)
Proof equivalence in MLL is PSPACE-complete
MLL proof equivalence is the problem of deciding whether two proofs in
multiplicative linear logic are related by a series of inference permutations.
It is also known as the word problem for star-autonomous categories. Previous
work has shown the problem to be equivalent to a rewiring problem on proof
nets, which are not canonical for full MLL due to the presence of the two
units. Drawing from recent work on reconfiguration problems, in this paper it
is shown that MLL proof equivalence is PSPACE-complete, using a reduction from
Nondeterministic Constraint Logic. An important consequence of the result is
that the existence of a satisfactory notion of proof nets for MLL with units is
ruled out (under current complexity assumptions). The PSPACE-hardness result
extends to equivalence of normal forms in MELL without units, where the
weakening rule for the exponentials induces a similar rewiring problem.Comment: Journal version of: Willem Heijltjes and Robin Houston. No proof nets
for MLL with units: Proof equivalence in MLL is PSPACE-complete. In Proc.
Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic
and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science, 201
Bigraphs with sharing
Bigraphical Reactive Systems (BRS) were designed by Milner as a universal formalism for modelling systems that evolve in time, locality, co-locality and connectivity. But the underlying model of location (the place graph) is a forest, which means there is no straightforward representation of locations that can overlap or intersect. This occurs in many domains, for example in wireless signalling, social interactions and audio communications. Here, we define bigraphs with sharing, which solves this problem by an extension of the basic formalism: we define the place graph as a directed acyclic graph, thus allowing a natural representation of overlapping or intersecting locations. We give a complete presentation of the theory of bigraphs with sharing, including a categorical semantics, algebraic properties, and several essential procedures for computation: bigraph with sharing matching, a SAT encoding of matching, and checking a fragment of the logic BiLog. We show that matching is an instance of the NP-complete sub-graph isomorphism problem and our approach based on a SAT encoding is also efficient for standard bigraphs. We give an overview of BigraphER (Bigraph Evaluator & Rewriting), an efficient implementation of bigraphs with sharing that provides manipulation, simulation and visualisation. The matching engine is based on the SAT encoding of the matching algorithm. Examples from the 802.11 CSMA/CA RTS/CTS protocol and a network management support system illustrate the applicability of the new theory
Effectively Solving NP-SPEC Encodings by Translation to ASP
NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe Prolog and via Boolean satisfiability solvers. In this paper, we present translations from NP-SPEC into ASP, and provide an experimental evaluation of existing implementations and the proposed translations to ASP using various ASP solvers. The results show that translating to ASP clearly has an edge over the existing translation into SAT, which involves an intrinsic grounding process. We also argue that it might be useful to incorporate certain language constructs of NPSPEC into mainstream ASP
Parameterized Complexity of Graph Constraint Logic
Graph constraint logic is a framework introduced by Hearn and Demaine, which
provides several problems that are often a convenient starting point for
reductions. We study the parameterized complexity of Constraint Graph
Satisfiability and both bounded and unbounded versions of Nondeterministic
Constraint Logic (NCL) with respect to solution length, treewidth and maximum
degree of the underlying constraint graph as parameters. As a main result we
show that restricted NCL remains PSPACE-complete on graphs of bounded
bandwidth, strengthening Hearn and Demaine's framework. This allows us to
improve upon existing results obtained by reduction from NCL. We show that
reconfiguration versions of several classical graph problems (including
independent set, feedback vertex set and dominating set) are PSPACE-complete on
planar graphs of bounded bandwidth and that Rush Hour, generalized to boards, is PSPACE-complete even when is at most a constant
On the proof complexity of Paris-harrington and off-diagonal ramsey tautologies
We study the proof complexity of Paris-Harrington’s Large Ramsey Theorem for bi-colorings of graphs and
of off-diagonal Ramsey’s Theorem. For Paris-Harrington, we prove a non-trivial conditional lower bound
in Resolution and a non-trivial upper bound in bounded-depth Frege. The lower bound is conditional on a
(very reasonable) hardness assumption for a weak (quasi-polynomial) Pigeonhole principle in RES(2). We
show that under such an assumption, there is no refutation of the Paris-Harrington formulas of size quasipolynomial
in the number of propositional variables. The proof technique for the lower bound extends the
idea of using a combinatorial principle to blow up a counterexample for another combinatorial principle
beyond the threshold of inconsistency. A strong link with the proof complexity of an unbalanced off-diagonal
Ramsey principle is established. This is obtained by adapting some constructions due to Erdos and Mills. ˝
We prove a non-trivial Resolution lower bound for a family of such off-diagonal Ramsey principles
Expressive Path Queries on Graph with Data
Graph data models have recently become popular owing to their applications,
e.g., in social networks and the semantic web. Typical navigational query
languages over graph databases - such as Conjunctive Regular Path Queries
(CRPQs) - cannot express relevant properties of the interaction between the
underlying data and the topology. Two languages have been recently proposed to
overcome this problem: walk logic (WL) and regular expressions with memory
(REM). In this paper, we begin by investigating fundamental properties of WL
and REM, i.e., complexity of evaluation problems and expressive power. We first
show that the data complexity of WL is nonelementary, which rules out its
practicality. On the other hand, while REM has low data complexity, we point
out that many natural data/topology properties of graphs expressible in WL
cannot be expressed in REM. To this end, we propose register logic, an
extension of REM, which we show to be able to express many natural graph
properties expressible in WL, while at the same time preserving the
elementariness of data complexity of REMs. It is also incomparable to WL in
terms of expressive power.Comment: 39 page
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