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Of all publications in the section: 4
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Article
Kontchakov R., Pratt-Hartmann I., Zakharyaschev M. Artificial Intelligence. 2014. Vol. 217. P. 43-75.

The language RCC8RCC8is a widely-studied formalism for describing topological arrangements of spatial regions. The variables of this language range over the collection of non-empty, regular closed sets of n  -dimensional Euclidean space, here denoted RC+(Rn)RC+(Rn), and its non-logical primitives allow us to specify how the interiors, exteriors and boundaries of these sets intersect. The key question is the satisfiability problem  : given a finite set of atomic RCC8RCC8-constraints in m variables, determine whether there exists an m  -tuple of elements of RC+(Rn)RC+(Rn)satisfying them. These problems are known to coincide for all n≥1n≥1, so that RCC8RCC8-satisfiability is independent of dimension. This common satisfiability problem is NLogSpace-complete. Unfortunately, RCC8RCC8lacks the means to say that a spatial region comprises a ‘single piece’, and the present article investigates what happens when this facility is added. We consider two extensions of RCC8RCC8: RCC8cRCC8c, in which we can state that a region is connected  , and RCC8c∘RCC8c∘, in which we can instead state that a region has a connected interior. The satisfiability problems for both these languages are easily seen to depend on the dimension n  , for n≤3n≤3. Furthermore, in the case of RCC8c∘RCC8c∘, we show that there exist finite sets of constraints that are satisfiable over RC+(R2)RC+(R2), but only by ‘wild’ regions having no possible physical meaning. This prompts us to consider interpretations over the more restrictive domain of non-empty, regular closed, polyhedral   sets, RCP+(Rn)RCP+(Rn). We show that (a) the satisfiability problems for RCC8cRCC8c(equivalently, RCC8c∘RCC8c∘) over RC+(R)RC+(R)and RCP+(R)RCP+(R)are distinct and both NP-complete; (b) the satisfiability problems for RCC8cRCC8cover RC+(R2)RC+(R2)and RCP+(R2)RCP+(R2)are identical and NP-complete; (c) the satisfiability problems for RCC8c∘RCC8c∘over RC+(R2)RC+(R2)and RCP+(R2)RCP+(R2)are distinct, and the latter is NP-complete. Decidability of the satisfiability problem for RCC8c∘RCC8c∘over RC+(R2)RC+(R2)is open. For n≥3n≥3, RCC8cRCC8cand RCC8c∘RCC8c∘are not interestingly different from RCC8RCC8. We finish by answering the following question: given that a set of RCC8cRCC8c- or RCC8c∘RCC8c∘-constraints is satisfiable over RC+(Rn)RC+(Rn)or RCP+(Rn)RCP+(Rn), how complex is the simplest satisfying assignment? In particular, we exhibit, for both languages, a sequence of constraints ΦnΦn, satisfiable over RCP+(R2)RCP+(R2), such that the size of ΦnΦngrows polynomially in n  , while the smallest configuration of polygons satisfying ΦnΦn cuts the plane into a number of pieces that grows exponentially. We further show that, over RC+(R2)RC+(R2), RCC8cRCC8c again requires exponentially large satisfying diagrams, while RCC8c∘RCC8c∘ can force regions in satisfying configurations to have infinitely many components.

 

 

Added: Mar 24, 2015
Article
Ianovski E., Ong L. Artificial Intelligence. 2018. No. 261. P. 1-15.

Boolean games allow us to succinctly represent strategic games with binary payoffs in the case where the players' preferences have a structure readily expressible in propositional logic. Since their introduction, the computational aspects of Boolean games have been of interest to the multiagent community, but so far the focus has been exclusively on pure strategy equilibria. In this paper we consider the complexity of problems involving mixed strategy equilibria, such as the existence of an equilibrium satisfying a given payoff constraint. The results are obtained by the observation that a mixed strategy can hold enough information to encode the computation history of an exponential time Turing machine.

Added: Feb 25, 2019
Article
Gottlob G., Kikot S., Kontchakov R. et al. Artificial Intelligence. 2014. Vol. 213. P. 42-59.

We give a solution to the succinctness problem for the size of first-order rewritings of conjunctive queries in ontology-based data access with ontology languages such as OWL 2 QL  , linear Datalog± and sticky Datalog±. We show that positive existential and nonrecursive datalog rewritings, which do not use extra non-logical symbols (except for intensional predicates in the case of datalog rewritings), suffer an exponential blowup in the worst case, while first-order rewritings can grow superpolynomially unless NP⊆P/poly. We also prove that nonrecursive datalog rewritings are in general exponentially more succinct than positive existential rewritings, while first-order rewritings can be superpolynomially more succinct than positive existential rewritings. On the other hand, we construct polynomial-size positive existential and nonrecursive datalog rewritings under the assumption that any data instance contains two fixed constants.

Added: Mar 24, 2015
Article
Gottlob G., Kikot S., Kontchakov R. et al. Artificial Intelligence. 2014. Vol. 213. P. 42-59.

We give a solution to the succinctness problem for the size of first-order rewritings of conjunctive queries in ontologybased data access with ontology languages such as OWL2QL, linear Datalog and sticky Datalog. We show that positive existential and nonrecursive datalog rewritings, which do not use extra non-logical symbols (except for intensional predicates in the case of datalog rewritings), su er an exponential blowup in the worst case, while first-order rewritings can grow superpolynomially unless NP in P/poly. We also prove that nonrecursive datalog rewritings are in general exponentially more succinct than positive existential rewritings, while first-order rewritings can be superpolynomially more succinct than positive existential rewritings. On the other hand, we construct polynomial-size positive existential and nonrecursive datalog rewritings under the assumption that any data instance contains two fixed constants.

Added: Oct 20, 2014