Showing papers in "Fundamenta Informaticae in 2002"

Approximate entropy reducts

Abstract: We use information entropy measure to extend the rough set based notion of a reduct. We introduce the Approximate Entropy Reduction Principle (AERP). It states that any simplification (reduction of attributes) in the decision model, which approximately preserves its conditional entropy (the measure of inconsistency of defining decision by conditional attributes) should be performed to decrease its prior entropy (the measure of the model's complexity). We show NP-hardness of optimization tasks concerning application of various modifications of AERP to data analysis.

Verifying epistemic properties of multi-agent systems via bounded model checking

Abstract: We present a framework for verifying temporal and epistemic properties of multi-agent systems by means of bounded model checking. We use interpreted systems as underlying semantics. We give details of the proposed technique, and show how it can be applied to the "attacking generals problem", a typical example of coordination in multi-agent systems.

Bounded Model Checking for the Universal Fragment of CTL

Abstract: Bounded Model Checking (BMC) has been recently introduced as an efficient verification method for reactive systems. BMC based on SAT methods consists in searching for a counterexample of a particular length and generating a propositional formula that is satisfiable iff such a counterexample exists. This new technique has been introduced by E. Clarke et al. for model checking of linear time temporal logic (LTL). Our paper shows how the concept of bounded model checking can be extended to ACTL (the universal fragment of CTL). The implementation of the algorithm for Elementary Net Systems is described together with the experimental results.

Collective intentions

Abstract: In this paper the notion of collective intention in teams of agents involved in cooperative problem solving (CPS) in multiagent systems (MAS) is investigated. Starting from individual intentions, goals, and beliefs defining agents' local asocial motivational and informational attitudes, we arrive at an understanding of collective intention in cooperative teams. The presented definitions are rather strong, in particular a collective intention implies that all members intend for all others to share that intention. Thus a team is created on the basis of collective intention, and exists as long as this attitude between team members exists, after which the group may disintegrate. For this reason it is crucial that collective intention lasts long enough.Collective intentions are formalized in a multi-modal logical framework. Completeness of this logic with respect to an appropriate class of Kripke models is proved. Two versions of collective intentions are discussed in the context of different situations. It is assumed that these definitions reflect solely vital aspects of motivational attitudes, leaving room for case-specific extensions. This makes the framework flexible and not overloaded. Together with individual and collective knowledge and belief, collective intention constitutes a basis for preparing a plan, reflected in the strongest attitude, i.e., in collective commitment, defined and investigated in our other papers.

Number-conserving cellular automaton rules

Abstract: A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established Two different forms of simpler and more visual representations of these rules are given, and their flow diagrams are determined Various examples are presented and applications to car traffic are indicated Two nontrivial three-state three-input self-conjugate rules have been found They can be used to model the dynamics of random walkers

On the Structure of Rough Approximations

Abstract: We study rough approximations based on indiscernibility relations which are not necessarily reflexive, symmetric or transitive. For this, we define in a lattice-theoretical setting two maps which mimic the rough approximation operators and note that this setting is suitable also for other operators based on binary relations. Properties of the ordered sets of the upper and the lower approximations of the elements of an atomic Boolean lattice are studied.

The Topological Structures of Membrane Computing

Abstract: In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes. Using an appropriate abstract setting, this technical device enables us to reformulate also the computation within a membrane and proposes a unified view on several computational mechanisms initially inspired by biological processes. These theoretical tools are instantiated in MGS, an experimental programming language handling various types of membrane structures in a homogeneous and uniform syntax.

RIONA: A New Classification System Combining Rule Induction and Instance-Based Learning

Abstract: The article describes a method combining two widely-used empirical approaches to learning from examples: rule induction and instance-based learning. In our algorithm (RIONA) decision is predicted not on the basis of the whole support set of all rules matching a test case, but the support set restricted to a neighbourhood of a test case. The size of the optimal neighbourhood is automatically induced during the learning phase. The empirical study shows the interesting fact that it is enough to consider a small neighbourhood to achieve classification accuracy comparable to an algorithm considering the whole learning set. The combination of k-NN and a rule-based algorithm results in a significant acceleration of the algorithm using all minimal rules. Moreover, the presented classifier has high accuracy for both kinds of domains: more suitable for k-NN classifiers and more suitable for rule based classifiers.

Learning rough set classifiers from gene expressions and clinical data

Abstract: Biological research is currently undergoing a revolution. With the advent of microarray technology the behavior of thousands of genes can be measured simultaneously. This capability opens a wide range of research opportunities in biology, but the technology generates a vast amount of data that cannot be handled manually. Computational analysis is thus a prerequisite for the success of this technology, and research and development of computational tools for microarray analysis are of great importance. One application of microarray technology is cancer studies where supervised learning may be used for predicting tumor subtypes and clinical parameters. We present a general Rough Set approach for classification of tumor samples analyzed with microarrays. This approach is tested on a data set of gastric tumors, and we develop classifiers for six clinical parameters. One major obstacle in training classifiers from microarray data is that the number of objects is much smaller that the number of attributes. We therefore introduce a feature selection method based on bootstrapping for selecting genes that discriminate significantly between the classes, and study the performance of this method. Moreover, the efficacy of several learning and discretization methods implemented in the ROSETTA system [18] is examined. Their performance is compared to that of linear and quadratic discrimination analysis. The classifiers are also biologically validated. One of the best classifiers is selected for each clinical parameter, and the connection between the genes used in these classifiers and the parameters are compared to the establish knowledge in the biomedical literature.

Institution-independent Ultraproducts

Abstract: We generalise the ultraproducts method from conventional model theory to an institution-independent (i.e. independent of the details of the actual logic formalised as an institution) framework based on a novel very general treatment of the semantics of some important concepts in logic, such as quantification, logical connectives, and ground atomic sentences. Unlike previous abstract model theoretic approaches to ultraproducts based on category theory, our work makes essential use of concepts central to institution theory, such as signature morphisms and model reducts. The institution-independent fundamental theorem on ultraproducts is presented in a modular manner, different combinations of its various parts giving different results in different logics or institutions. We present applications to institution-independent compactness, axiomatizability, and higher order sentences, and illustrate our concepts and results with examples from four different algebraic specification logics. In the introduction we also discuss the relevance of our institution-independent approach to the model theory of algebraic specification and computing science, but also to classical and abstract model theory.

Compact Suffix Array — A Space-Efficient Full-Text Index

Abstract: Suffix array is a widely used full-text index that allows fast searches on the text. It is constructed by sorting all suffixes of the text in the lexicographic order and storing pointers to the suffixes in this order. Binary search is used for fast searches on the suffix array. Compact suffix array is a compressed form of the suffix array that still allows binary searches, but the search times are also dependent on the compression. In this paper, we give efficient methods for constructing and querying compact suffix arrays. We also study practical issues, such as the trade off between compression and search times, and show how to reduce the space requirement of the construction. Experimental results are provided in comparison with other search methods. With a large text corpora, the index took 1.6 times the size of the text, while the searches were only two times slower than from a suffix array.

Checking Reachability Properties for Timed Automata via SAT

Abstract: The paper deals with the problem of checking reachability for timed automata. The main idea consists in combining the well-know forward reachability algorithm and the Bounded Model Checking (BMC) method. In order to check reachability of a state satisfying some desired property, first the transition relation of a timed automaton is unfolded iteratively to some depth and encoded as a propositional formula. Next, the desired property is translated to a propositional formula and the satisfiability of the conjunction of the two defined above formulas is checked. The unfolding of the transition relation can be terminated when either a state satisfying the property has been found or all the states of the timed automaton have been searched. The efficiency of the method is strongly supported by the experimental results.

Completeness of Timed μCRL

Abstract: In [25] a straightforward extension of the process algebra μCRL was proposed to explicitly deal with time. The process algebra μCRL has been especially designed to deal with data in a process algebraic context. Using the features for data, only a minor extension of the language was needed to obtain a very expressive variant of time. But [25] contains syntax, operational semantics and axioms characterising timed μCRL. It did not contain an in depth analysis of theory of timed μCRL. This paper fills this gap, by providing soundness and completeness results. The main tool to establish these is a mapping of timed to untimed μCRL and employing the completeness results obtained for untimed μCRL.

On the Injectivity of the Parikh Matrix Mapping

Abstract: In this paper we investigate the injectivity of the Parikh matrix mapping This research is done mainly on the binary alphabet We identify a family of binary words, refered to as ``palindromic amiable'', such that two such words are palindromic amiable if and only if they have the same image by the Parikh matrix mapping Some other related problems are discussed, too

On the classification and aggregation of hierarchies with different constitutive elements

Abstract: In this paper we present an aggregation method which can be applied to classifications having different vocabularies. The method uses the rank distance (Dinu, 2003), a metric which measures the similarity between two hierarchies based on the ranks of objects. We define the aggregation of n hierarchies as the classification for which the sum of distances from it to each of the n hierarchies is minimal. We study some of his rationality properties and propose some open problems.

Concept lattices and similarity in non-commutative fuzzy logic

Abstract: A classical (crisp) concept is given by its extent (a set of objects) and its intent (a set of properties) In commutative fuzzy logic, the generalization comes naturally, considering fuzzy sets of objects and properties In both cases (the first being actually a particular case of the second), the situation is perfectly symmetrical: a concept is given by a pair (A,B), where A is the largest set of objects sharing the attributes from B and B is the largest set of attributes shared by the objects from A (with the necessary nuance when fuzziness is concerned) Because of this symmetry, working with objects is the same as working with properties, so there is no need to make any choice In this paper, we define concepts in a "non-commutative fuzzy world", where conjunction of sentences is not necessarily commutative, which leads to the following non-symmetrical situation: a concept has one extent (because, at the end of the day, concepts are meant to embrace, using certain descriptions, diverse sets of objects), but two intents, given by the two residua (implications) of the non-commutative conjunction

On decomposition for incomplete data

Abstract: In this paper we present a method of data decomposition to avoid the necessity of reasoning on data with missing attribute values. This method can be applied to any algorithm of classifier induction. The original incomplete data is decomposed into data subsets without missing values. Next, methods for classifier induction are applied to these sets. Finally, a conflict resolving method is used to obtain final classification from partial classifiers. We provide an empirical evaluation of the decomposition method accuracy and model size with use of various decomposition criteria on data with natural missing values. We present also experiments on data with synthetic missing values to examine the properties of proposed method with variable ratio of incompleteness.

GP Systems with Forbidding Context

Abstract: We consider extended variants of GP systems, i.e., membrane systems with sequential applications of evolution rules. The main features we explore are applicability conditions (context conditions) on single objects as well as on the remaining contents of the underlying compartment. For a special very restricted variant only using forbidding context conditions we already obtain universal computational power.

Applying Rough Set Theory to Multi Stage Medical Diagnosing

Abstract: The work contains an example of application of Rough Set Theory to decision making - diagnosing Mitochondrial Encephalomyopathies (MEM) for children. The resulting decision support system maximally limits the indications for invasive diagnostic methods (puncture, muscle and/or nerve specimens). Moreover, it shortens the time necessary for making diagnosis. The system has been developed on the basis of data obtained from the II Clinic Department of Pediatrics of the Silesian Academy of Medicine (further referred to as the Clinic of Pediatrics).

A design of real-time non-regular sequence generation algorithms and their implementations on cellular automata with 1-bit inter-cell communications

Abstract: We introduce a special new class of cellular automata(CA) whose inter-cell communication is restricted to 1-bit. Several design examples for 1-bit inter-cell communication cellular algorithms are given. It is shown that infinite non-regular sequences such as {2^n | n = 1, 2, 3,..}, {n^2 |n = 1, 2, 3,..} and Fibonacci sequences can be generated in real-time by cellular automata with 1-bit inter-cell communications. In addition, twice real-time prime generation algorithm is also given.

P System Software Simulator

Abstract: We present a software application that is intended to be a tool for people working with P~systems. This software tool is called the Membrane Simulator and it provides a graphical simulation for two variants of P systems: the initial version of the catalytic hierarchical cell system and the active membrane system.

Rough sets and infomorphisms: towards approximation of relations in distributed environments

Abstract: We discuss the relationships between information systems and classifications as well as between infomorphisms and definability of relations (between whole objects and their parts) in information systems. Infomorphisms between information systems (classifications) IS_1 and IS_2 make it possible to define some formulas over IS_2 by means of formulas over IS_1. The remaining formulas over IS_2 can be approximatively defined by means of formulas over IS_1. The approximation operations are defined using the rough set approach. We present definitions and examples of such approximations.

Chaotic Subshifts and Related Languages Applications to one-dimensional Cellular Automata

Abstract: Subshift behaviors of one-dimensional (1D) bi-infinite Cellular Automata are studied. In particular the conditions under which subshifts generated by CA 1D dynamical systems exhibit some components of the chaotic behavior (in particular transitivity, topological mixing and strong transitivity) are investigated. A complete classification of all elementary (Boolean radius one) CA with respect to subshifts is given.

Shadowed sets and related algebraic structures

Abstract: BZMV^{dM} algebras are introduced as an abstract environment to describe both shadowed and fuzzy sets. This structure is endowed with two unusual complementations: a fuzzy one ¬ and an intuitionistic one ∼. Further, we show how to define in any BZMV^{dM} algebra the Boolean sub-algebra of exact elements and to give a rough approximation of fuzzy elements through a pair of exact elements using an interior and an exterior mapping. Then, we introduce the weaker notion of pre-BZMV^{dM} algebra. This structure still have as models fuzzy and shadowed sets but with respect to a weaker notion of intuitionistic negation ∼_α with α ∈ [0, h). In pre-BZMV^{dM} algebras it is still possible to define an interior and an exterior mapping but, in this case, we have to distinguish between open and closed exact elements. Finally, we see how it is possible to define α-cuts and level fuzzy sets in the pre-BZMV^{dM} algebraic context of fuzzy sets.

A new Bayesian tree learning method with reduced time and space complexity

Abstract: Bayesian networks have many practical applications due to their capability to represent joint probability distribution in many variables in a compact way. There exist efficient reasoning methods for Bayesian networks. Many algorithms for learning Bayesian networks from empirical data have been developed.A well-known problem with Bayesian networks is the practical limitation for the number of variables for which a Bayesian network can be learned in reasonable time. A remarkable exception here is the Chow/Liu algorithm for learning tree-like Bayesian networks. However, its quadratic time and space complexity in the number of variables may prove also prohibitive for high dimensional data.The paper presents a novel algorithm overcoming this limitation for the tree-like class of Bayesian networks. The new algorithm space consumption grows linearly with the number of variables n while the execution time is proportional to n. ln(n), hence both are better than those of Chow/Liu algorithm. This opens new perspectives in construction of Bayesian networks from data containing tens of thousands and more variables, e.g. in automatic text categorization.

A comparative study of some generalized rough approximations

Abstract: In this paper we focus upon a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to any binary reflexive relation. We aim at finding the best of several candidates for generalized rough approximation mappings, where both definability of sets by elementary granules of information as well as the issue of distinction among positive, negative, and border regions of a set are taken into account.

Evolution of Collective Commitment during Teamwork

Abstract: In this paper we aim to describe dynamic aspects of social and collective attitudes in teams of agents involved in Cooperative Problem Solving (CPS). Particular attention is given to the strongest motivational attitude, collective commitment, and its evolution during team action. First, building on our previous work, a logical framework is sketched in which a number of relevant social and collective attitudes is formalized, leading to the plan-based definition of collective commitments. Moreover, a dynamic logic component is added to this framework in order to capture the effects of the complex actions that are involved in the consecutive stages of CPS, namely potential recognition, team formation, plan formation and team action. During team action, the collective commitment leads to the execution of agent-specific actions. A dynamic and unpredictable environment may, however, cause the failure of some of these actions, or present the agents with new opportunities. The abstract reconfiguration algorithm, presented in a previous paper, is designed to handle the re-planning needed in such situations in an efficient way. In this paper, the dynamic logic component of the logical framework addresses issues pertaining to adjustments in collective commitment during the reconfiguration process.

Simulations of Photosynthesis by a $K$-Subset Transforming System with Membrane

Abstract: By considering the inner regions of living cells' membranes, P systems with inner regions are introduced. Then, a new type of membrane computing systems are considered, called $K$-subset transforming systems with membranes, which can treat nonintegral multiplicities of objects. As an application, a K-subset transforming system is proposed in order to model the light reactions of the photosynthesis. The behaviour of such systems is simulated on a computer.

Towards an Ontology of Approximate Reason

Abstract: This article introduces structural aspects in an ontology of approximate reason. The basic assumption in this ontology is that approximate reason is a capability of an agent. Agents are designed to classify information granules derived from sensors that respond to stimuli in the environment of an agent or received from other agents. Classification of information granules is carried out in the context of parameterized approximation spaces and a calculus of granules. Judgment in agents is a faculty of thinking about (classifying) the particular relative to decision rules derived from data. Judgment in agents is reflective, but not in the classical philosophical sense (e.g., the notion of judgment in Kant). In an agent, a reflective judgment itself is an assertion that a particular decision rule derived from data is applicable to an object (input). That is, a reflective judgment by an agent is an assertion that a particular vector of attribute (sensor) values matches to some degree the conditions for a particular rule. In effect, this form of judgment is an assertion that a vector of sensor values reflects a known property of data expressed by a decision rule. Since the reasoning underlying a reflective judgment is inductive and surjective (not based on a priori conditions or universals), this form of judgment is reflective, but not in the sense of Kant. Unlike Kant, a reflective judgment is surjective in the sense that it maps experimental attribute values onto the most closely matching descriptors (conditions) in a derived rule. Again, unlike Kant's notion of judgment, a reflective judgment is not the result of searching for a universal that pertains to a particular set of values of descriptors. Rather, a reflective judgment by an agent is a form of recognition that a particular vector of sensor values pertains to a particular rule in some degree. This recognition takes the form of an assertion that a particular descriptor vector is associated with a particular decision rule. These considerations can be repeated for other forms of classifiers besides those defined by decision rules.

Membrane systems with coupled transport: universality and normal forms

Abstract: This paper continues research on membrane systems which function by communication only, meaning that there are no evolving rules for molecules. The whole computation process relies on passage of molecules through membranes - this provides communication between regions of the membrane system. Next to transport of single molecules through membranes (uniport) we also study a coupled transport of molecules, with two molecules passing either in the same direction (symport) or in opposite directions (antiport). We study the computational power of such membrane systems and prove that using only symport one gets Turing universality. Moreover, we prove that five membranes suffice to get Turing universality, and the number of membranes can be decreased to three if forbidding context conditions for transport are used.