# Showing papers in "Fundamenta Informaticae in 2010"

••

TL;DR: An improved version of the algorithm for identification of the full set of truly important variables in an information system is presented, an extension of the random forest method which utilises the importance measure generated by the original algorithm.

Abstract: Machine learning methods are often used to classify objects described by hundreds of attributes; in many applications of this kind a great fraction of attributes may be totally irrelevant to the classification problem. Even more, usually one cannot decide a priori which attributes are relevant. In this paper we present an improved version of the algorithm for identification of the full set of truly important variables in an information system. It is an extension of the random forest method which utilises the importance measure generated by the original algorithm. It compares, in the iterative fashion, the importances of original attributes with importances of their randomised copies. We analyse performance of the algorithm on several examples of synthetic data, as well as on a biologically important problem, namely on identification of the sequence motifs that are important for aptameric activity of short RNA sequences.

346 citations

••

TL;DR: A flaw in the original PSO is identified which causes stagnation of the swarm, Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum and further extensions with provable global convergence are described.

Abstract: The Particle Swarm Optimiser (PSO) is a population based stochastic optimisation algorithm, empirically shown to be efficient and robust. This paper provides a proof to show that the original PSO does not have guaranteed convergence to a local optimum. A flaw in the original PSO is identified which causes stagnation of the swarm. Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum. Further extensions with provable global convergence are also described. Experimental results are provided to elucidate the behavior of the modified PSO as well as PSO variations with global convergence.

122 citations

••

TL;DR: In this paper, partial order reduction techniques for the verification of multi-agent systems are investigated for the case of interleaved interpreted systems, a particular class of interpreted systems in which only one action at the time is performed in the system.

Abstract: We investigate partial order reduction techniques for the verification of multi-agent systems. We investigate the case of interleaved interpreted systems. These are a particular class of interpreted systems, a mainstream MAS formalism, in which only one action at the time is performed in the system. We present a notion of stuttering-equivalence and prove the semantical equivalence of stuttering-equivalent traces with respect to linear and branching time temporal logics for knowledge without the next operator. We give algorithms to reduce the size of the models before the model checking step and show preservation properties. We evaluate the technique by discussing implementations and the experimental results obtained against well-known examples in the MAS literature.

56 citations

••

TL;DR: This paper is a brief case study of Backward Induction for extensive games, replacing earlier static logical definitions by stepwise dynamic ones, and shows how an abstract logical perspective can bring out basic invariant structure in games.

Abstract: Current methods for solving games embody a form of "procedural rationality" that invites logical analysis in its own right. This paper is a brief case study of Backward Induction for extensive games, replacing earlier static logical definitions by stepwise dynamic ones. We consider a number of analysis from recent years that look different conceptually, and find that they are all mathematically equivalent. This shows how an abstract logical perspective can bring out basic invariant structure in games. We then generalize this to an exploration of fixed-point logics on finite trees that best fit game-theoretic equilibria. We end with some open questions that suggest a broader program for merging current computational logics with notions and results from game theory. This paper is largely a program for opening up an area: an extended version of the technical results will be found in the forthcoming dissertation [26].

51 citations

••

TL;DR: The fundamental role of approximation spaces for inducing diverse kinds of classifiers used in machine learning or data mining is emphasized and the uniform foundations for inducing approximations of different kinds of granules are presented.

Abstract: We discuss some generalizations of the approximation space definition introduced in 1994 [24, 25]. These generalizations are motivated by real-life applications. Rough set based strategies for extension of such generalized approximation spaces from samples of objects onto their extensions are discussed. This enables us to present the uniform foundations for inducing approximations of different kinds of granules such as concepts, classifications, or functions. In particular, we emphasize the fundamental role of approximation spaces for inducing diverse kinds of classifiers used in machine learning or data mining.

46 citations

••

TL;DR: The type rules for a dependently typed core calculus are presented together with a straight-forward implementation in Haskell and the changes necessary to shift from a simply-typed lambda calculus to the dependent typed lambda calculus are highlighted.

Abstract: We present the type rules for a dependently typed core calculus together with a straight-forward implementation in Haskell We explicitly highlight the changes necessary to shift from a simply-typed lambda calculus to the dependently typed lambda calculus We also describe how to extend our core language with data types and write several small example programs The article is accompanied by an executable interpreter and example code that allows immediate experimentation with the system we describe

42 citations

••

TL;DR: The newest version of the MLEM2 algorithm for rule induction, a basic component of the LERS data mining system, is presented, based on local lower and upper approximations, and in its current form for the first time.

Abstract: In this paper, we present the newest version of the MLEM2 algorithm for rule induction, a basic component of the LERS data mining system. This version of the MLEM2 algorithm is based on local lower and upper approximations, and in its current formis presented in this paper for the first time. Additionally, we present results of experiments comparing the local version of the MLEM2 algorithm for rule induction with an older version of MLEM2, which was based on global lower and upper approximations. Our experiments show that the local version of MLEM2 is significantly better than the global version of MLEM2 (2% significance level, two-tailed Wilcoxon test).

41 citations

••

TL;DR: The main objective of this paper is to show how probe functions can provide new topologies on the quotient set U/E and, in consequence, new (perceptual)Topological links between perception of objects and classification of these objects.

Abstract: The paper aims to establish topological links between perception of objects (as it is defined in the framework of near sets) and classification of these objects (as it is defined in the framework of rough sets). In the near set approach, the discovery of near sets (i.e. sets containing objects with similar descriptions) starts with the selection of probe functions which provide a basis for describing and discerning objects. On the other hand, in the rough set approach, the classification of objects is based on object attributes which are collected into information systems (or data tables). As is well-known, an information system can be represented as a topological space (U, τ E). If we pass froman approximation space (U,E) to the quotient space U/E, where points represent indiscernible objects of U, then U/E will be endowed with the discrete topology induced (via the canonical projection) by τ E. The main objective of this paper is to show how probe functions can provide new topologies on the quotient set U/E and, in consequence, new (perceptual) topologies on U.

40 citations

••

TL;DR: This paper analyses the expressive power of two possibilistic counterparts to Jeffrey's rule for modeling belief revision in intelligent agents and shows that this rule can be used to recover several existing approaches proposed in knowledge base revision, such as adjustment, natural belief Revision, drastic belief revision, and the revision of an epistemic state by another epistemic states.

Abstract: Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey's rule, which extends conditioning to probabilistic inputs, is appropriate for revising probabilistic epistemic states when new information comes in the form of a partition of events with new probabilities and has priority over prior beliefs. This paper analyses the expressive power of two possibilistic counterparts to Jeffrey's rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover several existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, and the revision of an epistemic state by another epistemic state. In addition, we also show that some recent forms of revision, called improvement operators, can also be recovered in our framework.

37 citations

••

TL;DR: A sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection is provided and a new approach based on a generalization of Godel implication is proposed for building the complete lattice of all intervals-valued fuzzy formal concepts.

Abstract: Fuzzy formal concept analysis is concernedwith formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between a given object and a given property is a matter of degree in a scale L (generally [0,1]). However, the extent to which "object o has property a" may be sometimes hard to assess precisely. Then it is convenient to use a sub-interval from the scale L rather than a precise value. Such formal contexts naturally lead to interval-valued fuzzy formal concepts. The aim of the paper is twofold. We provide a sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, a new approach based on a generalization of Godel implication is proposed for building the complete lattice of all interval-valued fuzzy formal concepts.

35 citations

••

TL;DR: This work studies the notion of solvability in the resource calculus, an extension of the λ-calculus modelling resource consumption, and gives a syntactical, operational and logical characterization for the may-solvability and only a partial characterization of the must-solvable.

Abstract: We study the notion of solvability in the resource calculus, an extension of the λ-calculus modelling resource consumption. Since this calculus is non-deterministic, two different notions of solvability arise, one optimistic (angelical, may) and one pessimistic (demoniac, must). We give a syntactical, operational and logical characterization for the may-solvability and only a partial characterization of the must-solvability. Finally, we discuss the open problem of a complete characterization of the must-solvability.

••

TL;DR: It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFA with at least 2$^{n/2-2}$ states (the known upper bound is 2$^n), with witness languages given over an exponentially growing alphabet.

Abstract: It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFA with at least 2$^{n/2-2}$ states (the known upper bound is 2$^n$), with witness languages given over an exponentially growing alphabet. For a 3-letter alphabet, scattered substrings are shown to require at least 2$^{sqrt{2n+30}-6}$ states. A similar state complexity function for scattered superstrings is determined to be exactly 2$^{n-2}$ + 1 for an alphabet of at least n − 2 letters, and strictly less for any smaller alphabet. For a 3-letter alphabet, the state complexity of scattered superstrings is at least 1/5 4sqrt{n/2}n-3/4.

••

TL;DR: The notion of deterministic tiling system and the corresponding family of languages (DREC) and its structural and closure properties are introduced and it is shown that, in contrast with the one-dimensional case, there exist other classes between deterministic and non-deterministic families.

Abstract: Recognizable two-dimensional languages (REC) are defined by tiling systems that generalize to two dimensions non-deterministic finite automata for strings. We introduce the notion of deterministic tiling system and the corresponding family of languages (DREC) and study its structural and closure properties. Furthermore we show that, in contrast with the one-dimensional case, there exist other classes between deterministic and non-deterministic families that we separate by means of examples and decidability properties.

••

TL;DR: The framework is based on the ConDec graphical notation for modeling Business Processes, and on Abductive Logic Programming technology for verification of properties, and it is guaranteed to terminate when applied to models that contain loops.

Abstract: We discuss the static verification of declarative Business Processes. We identify four desiderata about verifiers, and propose a concrete framework which satisfies them. The framework is based on the ConDec graphical notation for modeling Business Processes, and on Abductive Logic Programming technology for verification of properties. Empirical evidence shows that our verification method seems to perform and scale better, in most cases, than other state of the art techniques (model checkers, in particular). A detailed study of our framework’s theoretical properties proves that our approach is sound and complete when applied to ConDec models that do not contain loops, and it is guaranteed to terminate when applied to models that contain loops.

••

TL;DR: This work proposes a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP), and applies several techniques to reduce the search space by symmetry breaking and positional relations of rectangles.

Abstract: We propose a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP) In this problem, we are given a set of rectangles and one large rectangle called a strip The goal of the problem is to pack all rectangles without overlapping, into the strip by minimizing the overall height of the packing Although the 2SPP has been studied in Operations Research, some instances are still hard to solve Our method solves the 2SPP by translating it into a SAT problem through a SAT encoding called order encoding The translated SAT problems tend to be large; thus, we apply several techniques to reduce the search space by symmetry breaking and positional relations of rectangles To solve a 2SPP, that is, to compute the minimum height of a 2SPP, we need to repeatedly solve similar SAT problems We thus reuse learned clauses and assumptions from the previously solved SAT problems To evaluate our approach, we obtained results for 38 instances from the literature and made comparisons with a constraint satisfaction solver and an ad-hoc 2SPP solver

••

TL;DR: An equational theory for Restricted Broadcast Process Theory is provided to reason about ad hoc networks and an extended algebra called Computed Network Theory is exploited to axiomatize restricted broadcast.

Abstract: We provide an equational theory for Restricted Broadcast Process Theory to reason about ad hoc networks. We exploit an extended algebra called Computed Network Theory to axiomatize restricted broadcast. It allows one to define the behavior of an ad hoc network with respect to the underlying topologies. We give a sound and ground-complete axiomatization for CNT terms with finite-state behavior, modulo what we call rooted branching computed network bisimilarity.

••

TL;DR: SLGAD resolution that computes the (conditional) probability of a ground query from a range-restricted LPAD and is based on SLG resolution for normal logic programs, which is compared with Ailog2 and SLDNFAD on the problems in which they do not go into infinite loops.

Abstract: Logic Programs with Annotated Disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of the well-founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause.
Inference on LPADs can be performed using either the system Ailog2, that was developed for the Independent Choice Logic, or SLDNFAD, an algorithm based on SLDNF. However, both of these algorithms run the risk of going into infinite loops and of performing redundant computations.
In order to avoid these problems, we present SLGAD resolution that computes the (conditional) probability of a ground query from a range-restricted LPAD and is based on SLG resolution for normal logic programs. As SLG, it uses tabling to avoid some infinite loops and to avoid redundant computations.
The performances of SLGAD are evaluated on classical benchmarks for normal logic programs under the well-founded semantics, namely a 2-person game and the ancestor relation, and on games of dice.
SLGAD is compared with Ailog2 and SLDNFAD on the problems in which they do not go into infinite loops, namely those that are described by a modularly acyclic program.
The results show that SLGAD is sometimes slower than Ailog2 and SLDNFAD but, if the program requires the repeated computations of the same goals, as for the dice games, then SLGAD is faster than both.

••

TL;DR: It is proved that, over the class of finitely branching trees, this extension of monadic second-order logic of order with the uncountability quantifier "there exist uncountably many sets" is equally expressive to plain monadicSecond-order Logic of order.

Abstract: We study an extension of monadic second-order logic of order with the uncountability quantifier "there exist uncountably many sets". We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order.
Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic.
Our approach is based on Shelah's composition method and uses basic results from descriptive set theory. The elimination result is constructive, yielding a decision procedure for the extended logic.

••

TL;DR: A new type-based approach to resource management, based on the use of dependent types to construct a Domain-Specific Embedded Language (DSEL) whose typing rules directly enforce the formal program properties that the authors require, to ensure strong static guarantees of correctness-by-construction.

Abstract: In the modern, multi-threaded, multi-core programming environment, correctly managing system resources, including locks and shared variables, can be especially difficult and errorprone A simple mistake, such as forgetting to release a lock, can have major consequences on the correct operation of a program, by, for example, inducing deadlock, often at a time and location that is isolated from the original error In this paper, we propose a new type-based approach to resource management, based on the use of dependent types to construct a Domain-Specific Embedded Language (DSEL) whose typing rules directly enforce the formal program properties that we require In this way, we ensure strong static guarantees of correctness-by-construction, without requiring the development of a new special-purpose type system or the associated special-purpose soundness proofs We also reduce the need for “over-serialisation”, the overly-conservative use of locks that often occurs in manually constructed software, where formal guarantees cannot be exploited We illustrate our approach by implementing a DSEL for concurrent programming and demonstrate its applicability with reference to an example based on simple bank account transactions

••

TL;DR: Combining cost function filtering with bound reasoning, the proposed DIMCTEf, an algorithm based on repeated executions of DMCTEF(r) with increasing r, which allows to alleviate their high size.

Abstract: Some distributed constraint optimization algorithms use a linear number of messages in the number of agents, but of exponential size. This is often the main limitation for their practical applicability. Here we present some distributed algorithms for these problems when they are arranged in a tree of agents. The exact algorithm, DCTE, computes the optimal solution but requires messages of size exp(s), where s is a structural parameter. Its approximate version, DMCTE(r), requires smaller messages of size exp(r), r < s, at the cost of computing approximate solutions. It provides a cost interval that bounds the error of the approximation. Using the technique of cost function filtering, we obtain DMCTEf(r). Combining cost function filtering with bound reasoning, we propose DIMCTEf, an algorithm based on repeated executions of DMCTEf(r) with increasing r. DIMCTEf uses messages of previous iterations to decrease the size of messages in the current iteration, which allows to alleviate their high size. We provide evidences of the benefits of our approach on two benchmarks.
This work has been partially supported by the project TIN2009-13591-C02-02.

••

TL;DR: This paper investigates a domain-independent method for plan adaptation that modifies the original plan by replanning within limited temporal windows containing portions of the plan that need to be revised.

Abstract: Fast plan adaptation is important in many AI applications. From a theoretical point of view, in the worst case adapting an existing plan to solve a new problem is no more efficient than a complete regeneration of the plan. However, in practice plan adaptation can be much more efficient than plan generation, especially when the adapted plan can be obtained by performing a limited amount of changes to the original plan. In this paper, we investigate a domain-independent method for plan adaptation that modifies the original plan by replanning within limited temporal windows containing portions of the plan that need to be revised. Each window is associated with a particular replanning subproblem that contains some “heuristic goals” facilitating the plan adaptation, and that can be solved using different planning methods. An experimental analysis shows that, in practice, adapting a given plan for solving a new problem using our techniques can be much more efficient than replanning from scratch.

••

TL;DR: A new algorithm solving the problem of edge-minimization for nondeterministic finite automata and some connected questions is formulated; this algorithm is a simplification of two ones published before.

Abstract: We consider in this paper the problem of edge-minimization for nondeterministic finite automata and some connected questions. We shall formulate a new algorithm solving this problem; this algorithm is a simplification of two ones published before. The connected problems include at first algorithms of combining states. We formulate some new sufficient conditions for the possibility of such combining.

••

TL;DR: This paper presents and study weakenings with PTIME data complexity of the instance checking problem for Horn knowledge bases in regular description logics and deals with the case when the constructor ∀ is allowed in premises of program clauses that are used as terminological axioms.

Abstract: Developing a good formalism and an efficient decision procedure for the instance checking problem is desirable for practical application of description logics. The data complexity of the instance checking problem is coNP-complete even for Horn knowledge bases in the basic description logic ALC. In this paper, we present and study weakenings with PTIME data complexity of the instance checking problem for Horn knowledge bases in regular description logics. We also study cases when the weakenings are an exact approximation. In contrast to previous related work of other authors, our approach deals with the case when the constructor ∀ is allowed in premises of program clauses that are used as terminological axioms.

••

TL;DR: Different variants of EOS safeness are defined, discuss their relationships, show that they all coincide for p/t-like EOS, and address the complexity of well known Petri net problems like reachability and liveness for this new class of object nets.

Abstract: In this paper we discuss the concept of safeness for Elementary Object Nets (EOS). Object nets are Petri nets which have Petri nets as tokens - an approach known as the nets-within-nets paradigm. Object nets are called elementary if the net system has a two levelled structure. The well known p/t nets can be considered as a special case of EOS. For p/t nets the concept of safeness means that there is at most one token on each place. Since object nets have nested markings there are different possibilities to generalise this idea for EOS. In this paper we define different variants of EOS safeness, discuss their relationships, show that they all coincide for p/t-like EOS, and address the complexity of well known Petri net problems like reachability and liveness for this new class of object nets.

••

TL;DR: This work proposes the first bit-parallel algorithm computing a CLCS and/or its length which outperforms the other known algorithms in terms of speed.

Abstract: The problem of finding a constrained longest common subsequence (CLCS) for the sequences A and B with respect to the sequence P was introduced recently. Its goal is to find a longest subsequence C of A and B such that P is a subsequence of C. Most of the algorithms solving the CLCS problem are based on dynamic programming. Bit-parallelism is a technique of using single bits in a machine word for concurrent computation. We propose the first bit-parallel algorithm computing a CLCS and/or its length which outperforms the other known algorithms in terms of speed.

••

TL;DR: In order to prove the relevance of the proposed rough entropy measures, the evaluation of rough entropy segmentations based on the comparison with human segmentations from Berkeley and Weizmann image databases has been presented and seems to comprehend properly properties validated by different image segmentation quality indices.

Abstract: High quality performance of image segmentation methods presents one leading priority in design and implementation of image analysis systems. Incorporating the most important image data information into segmentation process has resulted in development of innovative frameworks such as fuzzy systems, rough systems and recently rough - fuzzy systems. Data analysis based on rough and fuzzy systems is designed to apprehend internal data structure in case of incomplete or uncertain information. Rough entropy framework proposed in [12,13] has been dedicated for application in clustering systems, especially for image segmentation systems. We extend that framework into eight distinct rough entropy measures and related clustering algorithms. The introduced solutions are capable of adaptive incorporation of the most important factors that contribute to the relation between data objects and makes possible better understanding of the image structure. In order to prove the relevance of the proposed rough entropy measures, the evaluation of rough entropy segmentations based on the comparison with human segmentations from Berkeley and Weizmann image databases has been presented. At the same time, rough entropy based measures applied in the domain of image segmentation quality evaluation have been compared with standard image segmentation indices. Additionally, rough entropy measures seem to comprehend properly properties validated by different image segmentation quality indices.

•

[...]

TL;DR: It is proved that the algebraic ordinals are exactly the ordinals less than ω, where ω is the number of fixed point equations in the LaSalle inequality.

Abstract: An algebraic tree T is one determined by a finite system of fixed point equations. The frontier Fr(T ) of an algebraic tree T is linearly ordered by the lexicographic order

••

TL;DR: It is proved that the data complexity of the instance checking problem in PDL is coNP-complete and the first ExpTime (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox is given.

Abstract: We reformulate Pratt’s tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and its implementation is more direct. Extending the method we give the first ExpTime (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic). We also prove a new result that the data complexity of the instance checking problem in PDL is coNP-complete.

••

Polytech'Savoie

^{1}TL;DR: This paper extends an existing dependent type theory having nice properties, with context-based rules and appropriate inductive types, and claims that the resulting theory exploiting the power of dependent types is able to provide a very expressive system together with a unified theory allowing higher-order reasoning.

Abstract: In the area of knowledge representation, a challenging topic is the formalization of context knowledge on the basis of logical foundations and ontological semantics. However, most attempts to provide a formal model of contexts suffer from a number of difficulties, such as limited expressiveness of representation, restricted variable quantification, lack of (meta) reasoning about properties, etc. In addition, type theory originally developed for formal modeling of mathematics has also been successfully applied to the correct specification of programs and in the semantics of natural language. In this paper, we suggest a type theoretical approach to the problem of context and action modeling. Type theory is used both for representing the system's knowledge of the discourse domain and for reasoning about it. For that purpose, we extend an existing dependent type theory having nice properties, with context-based rules and appropriate inductive types. We claim that the resulting theory exploiting the power of dependent types is able to provide a very expressive system together with a unified theory allowing higher-order reasoning.

••

TL;DR: The category having such spaces as objects is shown to be a topological construct (its initial and final structures are provided explicitly) and the lattice structure of the family of all these spaces is discussed.

Abstract: The present paper is devoted to the study of grill determined L-approachmerotopological spaces. The category having such spaces as objects is shown to be a topological construct (its initial and final structures are provided explicitly). The lattice structure of the family of all these spaces is also discussed. In the classical theory, this category (that is, when L={0, 1}) is a supercategory of the category of pseudo metric spaces and nonexpansive maps.