We present a second order logic of proportional quantifiers, SOLP, which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r–tuples of a model that satisfy a formula. Our logic is capable of expressing proportional versions of different problems of complexity up to NP-hard, a...

We investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless p = np. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enumerating minimal transversals of a given hypergraph. We...

The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME = NP, the model-checking problem for monadic second-order logic on finite words is...

The following operation has frequently occurred in mathematics and its applications: partition a set into several disjoint non-empty subsets, so that the elements in each partition subset are homogeneous or indistinguishable with respect to some given properties. H.-D.Ebbinghaus first (in 1991) distilled from this phenomenon, which is a monadic second order property in nature, a special kind of...

We use the category of presheaves over PTIME-functions in order to show that Cook and Urquhart's higher-order function algebra PV ! deenes exactly the PTIME-functions. As a byproduct we obtain a syntax-free generalisation of PTIME-computability to higher types. By restricting to sheaves for a suitable topology we obtain a model for intuitionistic predicate logic with b 1-induction over PV ! and...

Multisets are the fundamental data structure of P systems [12]. In this paper we relate P systems with the language and theory for multisets presented in [5]. This allows us, on the one hand, to define and implement P systems using multiset constraints in a constraint logic programming framework, and, on the other hand, to define and implement constraint solving procedures used to test multiset...

We investigate the complexity of axiom pinpointing for different members of the DL-Lite family of Description Logics. More precisely, we consider the problem of enumerating all minimal subsets of a given DL-Lite knowledge base that have a given consequence. We show that for theDL-Litecore,DL-Litekrom andDLLiteHN horn fragments such minimal subsets are efficiently enumerable with polynomial dela...

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approx...

Two isostructural 2D assemblies composed of [Ru2(O2CCF3)4] and TCNQ or TCNQF4 in a 2:1 ratio were synthesized: [{Ru2(O2CCF3)4}2TCNQ].3(p-xylene) (1b) and [{Ru2(O2CCF3)4}2TCNQF4].3(p-xylene) (2). In 1b, the TCNQ moiety is assigned to be neutral because of no significant electron transfer from the Ru24+ units. Therefore, the magnetic property of 1b can be understood to be a paramagnetic nature of...

The paper introduces LOGAN-H —a system for learning first-order function-free Horn expressions from interpretations. The system is based on an algorithm that learns by asking questions and that was proved correct in previous work. The current paper shows how the algorithm can be implemented in a practical system, and introduces a new algorithm based on it that avoids interaction and learns from...