The complexity of admissible rules of {\L}ukasiewicz logic

We investigate the computational complexity of admissibility of inference rules in infinite-valued {\L}ukasiewicz propositional logic (\L). It was shown in [13] that admissibility in {\L} is checkable in PSPACE. We establish that this result is optimal, i.e., admissible rules of {\L} are PSPACE-complete. In contrast, derivable rules of {\L} are known to be coNP-complete.Comment: 14 pages, 2 figures; to appear in Journal of Logic and Computatio

Assume-Admissible Synthesis

In this paper, we introduce a novel rule for synthesis of reactive systems, applicable to systems made of n components which have each their own objectives. It is based on the notion of admissible strategies. We compare our novel rule with previous rules defined in the literature, and we show that contrary to the previous proposals, our rule defines sets of solutions which are rectangular. This property leads to solutions which are robust and resilient. We provide algorithms with optimal complexity and also an abstraction framework.Comment: 31 page

Generic Modal Cut Elimination Applied to Conditional Logics

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature

Thick 2D Relations for Document Understanding

We use a propositional language of qualitative rectangle relations to detect the reading order from document images. To this end, we define the notion of a document encoding rule and we analyze possible formalisms to express document encoding rules such as LATEX and SGML. Document encoding rules expressed in the propositional language of rectangles are used to build a reading order detector for document images. In order to achieve robustness and avoid brittleness when applying the system to real life document images, the notion of a thick boundary interpretation for a qualitative relation is introduced. The framework is tested on a collection of heterogeneous document images showing recall rates up to 89%

Functional Complexity Measure for Networks

We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their vertices and a rewiring of their edges under certain constraints. The application will be a classification of networks in artificial or biological systems, where functionality plays a central role.Comment: 11 pages, LaTeX2e, 5 PostScript figure

Answer Set Planning Under Action Costs

Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language Kc, which extends the declarative planning language K by action costs. Kc provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing ``shortest'' plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language Kc and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved