Peter Vojtáš

Fuzzy logic programming

In this paper we consider the theory of fuzzy logic programming without negation. Our results cover logical systems with a wide variety of connectives ranging from t-norm and conorms, through conjunctors and disjunctors and their residuals to aggregation operators. Rules of our programs are many valued implications. We emphasize, that in contrast to other approaches, our logic is truth functional, i.e. according to P. Hajek, we work in fuzzy logic in narrow sense. We prove the soundness and the completeness of our formal model. We deal with applications to threshold computation, abduction, fuzzy unification based on similarity. We show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying.

Similarity-Based Unification: A Multi-Adjoint Approach

The aim of this paper is to build a formal model for similarity-based fuzzy unification in multi-adjoint logic programs. Specifically, a general framework of logic programming which allows the simultaneous use of different implications in the rules and rather general connectives in the bodies is introduced, then a procedural semantics for this framework is presented, and an approximative-completeness theorem proved. On this computational model, a similarity-based unification approach is constructed by simply adding axioms of fuzzy similarities and using classical crisp unification which provides a semantic framework for logic programming with different notions of similarity.

A Procedural Semantics for Multi-adjoint Logic Programming

Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, a procedural semantics is given for the paradigm of multiadjoint logic programming and completeness theorems are proved.

SOFSEM 2005: Theory and Practice of Computer Science

Invited Talks.- Discovering Treewidth.- From Research Prototypes to Industrial Strength Open Source Products - The ObjectWeb Experience.- How Hard Is It to Take a Snapshot?.- Logical Foundations for Data Integration.- Recent Advances in Graph Drawing.- The Hyperdatabase Network - New Middleware for Searching and Maintaining the Information Space.- Architecture of a Business Framework for the .NET Platform and Open Source Environments.- Progress on Crossing Number Problems.- Full Contributed Papers.- Greedy Differential Approximations for Min Set Cover.- A Methodology of Visual Modeling Language Evaluation.- Local Computations on Closed Unlabelled Edges: The Election Problem and the Naming Problem.- A Hierarchical Markovian Mining Approach for Favorite Navigation Patterns.- Non-planar Orthogonal Drawings with Fixed Topology.- A Topology-Driven Approach to the Design of Web Meta-search Clustering Engines.- Computing Upward Planar Drawings Using Switch-Regularity Heuristics.- Serial and Parallel Multilevel Graph Partitioning Using Fixed Centers.- Two-Layer Planarization: Improving on Parameterized Algorithmics.- On the Stability of Approximation for Hamiltonian Path Problems.- Robustness of Composed Timed Systems.- Topology Generation for Web Communities Modeling.- Recursion Versus Replication in Simple Cryptographic Protocols.- Modeling Data Integration with Updateable Object Views.- Fixed-Parameter Tractable Algorithms for Testing Upward Planarity.- Read/Write Based Fast-Path Transformation for FCFS Mutual Exclusion.- Adjustment of Indirect Association Rules for the Web.- Anonymous Communication with On-line and Off-line Onion Encoding.- Characteristic Patterns for LTL.- Planar Straight-Line Drawing in an Grid with Angular Resolution (1/n).- Modeling Nested Relationships in XML Documents Using Relational Databases.- RAQ: A Range-Queriable Distributed Data Structure.- On Some Weighted Satisfiability and Graph Problems.- On the Security and Composability of the One Time Pad.- Lower Bounds on the OBDD Size of Graphs of Some Popular Functions.- XML-Based Declarative Access Control.- VCD: A Visual Formalism for Specification of Heterogeneous Software Architectures.- Cost-Constrained Minimum-Delay Multicasting.- Ontology-Based Inconsistency Management of Software Requirements Specifications.- The Best Student Paper.- Suffix Tree Based Data Compression.- Short Contributed Papers.- Tier Aspect Model Based on Updatable Views.- Well-Founded Metamodeling for Model-Driven Architecture.- Stepwise Optimization Method for k-CNN Search for Location-Based Service.- An Approach for Integrating Analysis Patterns and Feature Diagrams into Model Driven Architecture.- Outerplanar Crossing Numbers of 3-Row Meshes, Halin Graphs and Complete p-Partite Graphs.- Fast Bit-Vector Algorithms for Approximate String Matching Under Indel Distance.- Feature Selection by Reordering.- A Management Scheme for the Basic Types in High Level Languages.- Bayesian Networks in Software Maintenance Management.- A Multiagent System Aiding Information Retrieval in Internet Using Consensus Methods.- Interval-Valued Data Structures and Their Application to e-Learning.- Boolean Functions with a Low Polynomial Degree and Quantum Query Algorithms.- Representation of Extended RBAC Model Using UML Language.- A Methodology for Writing Class Contracts.- Volumes of 3D Drawings of Homogenous Product Graphs.

A comparison of fuzzy and annotated logic programming

The aim of this paper is to contribute to the study of relationships between different formalism for handling uncertainty in logic programming, knowledge-based systems and deductive databases. Generalized annotated programs with restricted semantics (RGA-programs) are well suited to fit real-world data. We show that RGA-programs with constant annotations in body are equivalent to programs with left discontinuous annotation and with possibly non-computable semantics. Our model of fuzzy logic programming (FLP) can well handle recursive programs. We show that FLP has the same expressive power as RGA-programs without constant annotations in body of rules. We introduce several syntactical transformations of programs and study their models and production operators. We introduce a new efficient procedural semantics for RGA-programs and show connections between different sorts of computed answers.

Towards Biresiduated Multi-adjoint Logic Programming

Multi-adjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified through the study of a very intuitive family of operators, which turn out to be not necessarily commutative and associative and, thus, might have two different residuated implications; finally, we introduce the framework of biresiduated multi-adjoint logic programming and sketch some considerations on its fixpoint semantics.

Ordinal classification with monotonicity constraints

Classification methods commonly assume unordered class values. In many practical applications – for example grading – there is a natural ordering between class values. Furthermore, some attribute values of classified objects can be ordered, too. The standard approach in this case is to convert the ordered values into a numeric quantity and apply a regression learner to the transformed data. This approach can be used just in case of linear ordering. The proposed method for such a classification lies on the boundary between ordinal classification trees, classification trees with monotonicity constraints and multi-relational classification trees. The advantage of the proposed method is that it is able to handle non-linear ordering on the class and attribute values. For the better understanding, we use a toy example from the semantic web environment – prediction of rules for the users evaluation of hotels.

Induction of Fuzzy and Annotated Logic Programs

The new direction of the research in the field of data mining is the development of methods to handle imperfection (uncertainty, vagueness, imprecision,...). The main interest in this research is focused on probability models. Besides these there is an extensive study of the phenomena of imperfection in fuzzy logic. In this paper we concentrate especially on fuzzy logic programs (FLP) and Generalized Annotated Programs (GAP). The lack of the present research in the field of fuzzy inductive logic programming (FILP) is that every approach has its own formulation of the proof-theoretic part (often dealing with linguistic hedges) and lack sound and compete formulation of semantics. Our aim in this paper is to propose a formal model of FILP and induction of GAP programs (IGAP) based on sound and complete model of FLP (without linguistic hedges) and its equivalence with GAP. We focus on learning from entailment setting in this paper. We describe our approach to IGAP and show its consistency and equivalence to FILP. Our inductive method is used for detection of user preferences in a web search application. Finally, we compare our approach to several fuzzy ILP approaches.

UPRE: User Preference Based Search System

We present a middleware system UPRE enabling personalized Web search for users with different preferences. The input for UPRE is user evaluation of some objects in scale from the worst to the best. Our model is inspired by existing models of distributed middleware search. We use both inductive and deductive tasks to find user preferences and consequently best objects

A system recommending top-k objects for multiple users preferences

We discuss models of user preferences in Web environment. We construct a model for user preference querying over a number of data sources and ordering of answers by a combination of particular attribute rankings. We generalize Fagins algorithm in two directions - we develop some new heuristics for top-k search in the model without random access and propose a method of ordering lists of objects by user fuzzy function. To enable different user preferences our system does not require objects to be sorted -instead we use a B+-tree on each of the attribute domains. This leads to a more realistic model of Web services. We implement our methods and heuristics for search of top-k answers into Tokaf middleware framework prototype. We describe experiments with Tokaf and compare different performance measures with some other methods.