459 research outputs found
The Complexity of Reasoning for Fragments of Default Logic
Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified
the complexity of the extension existence problem for propositional default
logic as \SigmaPtwo-complete, and the complexity of the credulous and
skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete.
Additionally, he investigated restrictions on the default rules, i.e.,
semi-normal default rules. Selman made in 1992 a similar approach with
disjunction-free and unary default rules. In this paper we systematically
restrict the set of allowed propositional connectives. We give a complete
complexity classification for all sets of Boolean functions in the meaning of
Post's lattice for all three common decision problems for propositional default
logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-,
P-, NL-complete, trivial) for the extension existence problem, while for the
credulous and skeptical reasoning problem we obtain similar classifications
without trivial cases.Comment: Corrected versio
The XY Model and the Three-state Antiferromagnetic Potts model in Three Dimensions: Critical Properties from Fluctuating Boundary Conditions
We present the results of a Monte Carlo study of the three-dimensional XY
model and the three-dimensional antiferromagnetic three-state Potts model. In
both cases we compute the difference in the free energies of a system with
periodic and a system with antiperiodic boundary conditions in the
neighbourhood of the critical coupling. From the finite-size scaling behaviour
of this quantity we extract values for the critical temperature and the
critical exponent nu that are compatible with recent high statistics Monte
Carlo studies of the models. The results for the free energy difference at the
critical temperature and for the exponent nu confirm that both models belong to
the same universality class.Comment: 13 pages, latex-file+2 ps-files KL-TH-94/8 and CERN-TH.7290/9
Critical behavior of the planar magnet model in three dimensions
We use a hybrid Monte Carlo algorithm in which a single-cluster update is
combined with the over-relaxation and Metropolis spin re-orientation algorithm.
Periodic boundary conditions were applied in all directions. We have calculated
the fourth-order cumulant in finite size lattices using the single-histogram
re-weighting method. Using finite-size scaling theory, we obtained the critical
temperature which is very different from that of the usual XY model. At the
critical temperature, we calculated the susceptibility and the magnetization on
lattices of size up to . Using finite-size scaling theory we accurately
determine the critical exponents of the model and find that =0.670(7),
=1.9696(37), and =0.515(2). Thus, we conclude that the
model belongs to the same universality class with the XY model, as expected.Comment: 11 pages, 5 figure
Coverings and matchings in r-partite hypergraphs
Ryser\u27s conjecture postulates that for r -partite hypergraphs, Ï â€ (r - 1)Îœ where Ï is the covering number of the hypergraph and Îœ is the matching number. Although this conjecture has been open since the 1960s, researchers have resolved it for special cases such as for intersecting hypergraphs where r †5. In this article, we prove several results pertaining to matchings and coverings in r -partite intersecting hypergraphs. First, we prove that finding a minimum cardinality vertex cover for an r -partite intersecting hypergraph is NP-hard. Second, we note Ryser\u27s conjecture for intersecting hypergraphs is easily resolved if a given hypergraph does not contain a particular subhypergraph, which we call a âtornado.â We prove several bounds on the covering number of tornados. Finally, we prove the integrality gap for the standard integer linear programming formulation of the maximum cardinality r -partite hypergraph matching problem is at least r - k where k is the smallest positive integer such that r - k is a prime power
On the Substitution of Identicals in Counterfactual Reasoning
It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals with possible antecedents are transparencyâpreserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilistâfriendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized
Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model
on the three-dimensional simple cubic lattice with nearest neighbour
interactions. For this purpose, we use Monte Carlo simulations in connection
with a finite size scaling method. We find that there exists a finite value of
the coupling lambda^*, for both values of N, where leading corrections to
scaling vanish. As a first application, we compute the critical exponents
nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for
N=4.Comment: 21 pages, 2 figure
Efficiency in Multi-objective Games
In a multi-objective game, each agent individually evaluates each overall
action-profile on multiple objectives. I generalize the price of anarchy to
multi-objective games and provide a polynomial-time algorithm to assess it.
This work asserts that policies on tobacco promote a higher economic
efficiency
Global Inverse Consistency for Interactive Constraint Satisfaction
International audienceSome applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples
Block Spin Effective Action for 4d SU(2) Finite Temperature Lattice Gauge Theory
The Svetitsky-Yaffe conjecture for finite temperature 4d SU(2) lattice gauge
theory is confirmed by observing matching of block spin effective actions of
the gauge model with those of the 3d Ising model. The effective action for the
gauge model is defined by blocking the signs of the Polyakov loops with the
majority rule. To compute it numerically, we apply a variant of the IMCRG
method of Gupta and Cordery.Comment: LaTeX2e, 22 pages, 8 Figure
A constrained Potts antiferromagnet model with an interface representation
We define a four-state Potts model ensemble on the square lattice, with the
constraints that neighboring spins must have different values, and that no
plaquette may contain all four states. The spin configurations may be mapped
into those of a 2-dimensional interface in a 2+5 dimensional space. If this
interface is in a Gaussian rough phase (as is the case for most other models
with such a mapping), then the spin correlations are critical and their
exponents can be related to the stiffness governing the interface fluctuations.
Results of our Monte Carlo simulations show height fluctuations with an
anomalous dependence on wavevector, intermediate between the behaviors expected
in a rough phase and in a smooth phase; we argue that the smooth phase (which
would imply long-range spin order) is the best interpretation.Comment: 61 pages, LaTeX. Submitted to J. Phys.
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