Logics for Rough Concept Analysis

Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a ‘nondistributive’ (i.e. general lattice-based) setting.https://digitalcommons.chapman.edu/scs_books/1060/thumbnail.jp

Logics for Rough Concept Analysis

Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a `nondistributive' (i.e. general lattice-based) setting

Towards Static Analysis of Functional Programs using Tree Automata Completion

This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of terms reachable by a rewriting relation. The completion algorithm we focus on is parameterized by a set E of equations controlling the precision of the approximation and influencing its termination. For completion to be used as a static analysis, the first step is to guarantee its termination. In this work, we thus give a sufficient condition on E and T(F) for completion algorithm to always terminate. In the particular setting of functional programs, this condition can be relaxed into a condition on E and T(C) (terms built on the set of constructors) that is closer to what is done in the field of static analysis, where abstractions are performed on data.Comment: Proceedings of WRLA'14. 201

Data-Driven Abstraction

Given a program analysis problem that consists of a program and a property of interest, we use a data-driven approach to automatically construct a sequence of abstractions that approach an ideal abstraction suitable for solving that problem. This process begins with an infinite concrete domain that maps to a finite abstract domain defined by statistical procedures resulting in a clustering mixture model. Given a set of properties expressed as formulas in a restricted and bounded variant of CTL, we can test the success of the abstraction with respect to a predefined performance level. In addition, we can perform iterative abstraction-refinement of the clustering by tuning hyperparameters that determine the accuracy of the cluster representations (abstract states) and determine the number of clusters. Our methodology yields an induced abstraction and refinement procedure for property verification

Activating Generalized Fuzzy Implications from Galois Connections

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.F.J. Valverde-Albacete—was partially supported by EU FP7 project LiMoSINe, (contract 288024). C. Peláez-Moreno—was partially supported by the Spanish Government-CICYT project 2011-268007/TEC.Publicad