I am an associate professor at the Department of Computer science, Faculty of Science of the Pavol Jozef Safarik University in Kosice, Slovakia, research fellow of the Mathematical Institute of the Slovak Academy of Sciences and research fellow at Institute of Computer Sciences of Czech Academy of Sciences.
Previously I have worked mailnly in set theory, especialy in applications of set theory in real analysis, general topology and theoretical computer science.
Recently I am working in computer sciences. My main interest is in fuzzy logic programming and flexible querying. Results obtained so far cover soundness and completeness of various fuzzy logic programming and resolution systems, especially with arbitrary finite approximations of connectives, fuzzy abduction for descision making coupled with linear programming for cheapest solution. Flexible querying is covered by results on various types of fuzzy unification including second-order logic which is used to extend this theory to meta-data and at the end to extend the flexibility of our query system to include the capability of providing answers to natural language queries and finding the appropriate access methods even through the user does not know about them.
The research group led by Associate Professor Peter Vojtáš consists of experienced researchers covering a broad collection of soft computing and related areas and focused on model development and implementation of methods for extracting knowledge from uncertain and vague data contained in large and possibly distributed databases and flexible querying. The topics include fuzzy logic (Vojtáš), neural networks (Andrejková), database analysis and design (Vinar), computer networks (Jirásek), computer simulation methods and operations research in general (Kyselovic), design of information systems (Mihók, Semanišin), problems of combinatorial structures (Geffert), statistics (Zezula) or hypermedia (Vinar). Fuzzy logic programming and flexible querying. The results obtained so far cover soundness and completeness of various fuzzy logic programming and resolution systems, especially with arbitrary finite approximations of connectives, fuzzy abduction for decision making coupled with linear programming for cheapest solution. Flexible querying is covered by results on various types of fuzzy unification including second - order logic which is used to extend this theory to meta-data and at the end to extend the flexibility of our query system to include the capability of providing answers to natural language queries and finding the appropriate access methods even though the user does not know about them. Work done on structural complexity and combinatorial optimization where many fundamental results have already been obtained may conceivably be useful in considering the efficiency of various query optimization algorithms Database design and analysis. Our expertise covers IT knowledge and skills in various database and CASE tools and programming languages and interface and communication standards. The language of logic is used to provide the possibility of quickly constructing trial versions of sophisticated query analysis, implementation and optimization systems to test the basic approaches before creating the final version. Models for detection of similar records in distributed databases are studied too.
Multimedia, Hypermedia. Hypermedia is commonly thought of only in the context of web pages, teaching software etc.) Some preliminary results suggest the possibility of using them in a neglected area of making the output of software systems more user friendly by providing the option to produce output in hypermedia form linked to "resident textbooks".
Artificial neural networks. Prediction capability of neural networks (NN) was studied together with the topology of NN depending on the solved problem and from the research point of view very interesting problem of their topological adaptability (it means, the topology of NN is adapted according to solved problem). For feed-forward NN can be used incremental topology, for recurrent NN genetic algorithms.
Statistical data acquisition and simulation models. The use of statistical and heuristical methods in simulation models was studied and extensively applied. Statistical multivariate linear models and knowledge acquisition was examined.
The members of the group have - jointly or separately - worked on the subjects named, published many papers some of which (chosen for their possible relevance to the project in hand) are listed below, participated - often as invited speakers - in domestic and international conferences. Thus for instance P.Vojtáš was one of the organizers of the Workshop on much valued logic for CS applications at ECAI98 and together with G.Andrejková and A. Kyselovič they organized conferences, seminars and sections devoted to above subjects. A list of the large-scale projects in which the members have participated in various capacities would include personnel and payroll management systems for state and public administration (Vinar), information systems developed for the Slovak Gas Industry (Semanišin), Slovak Tax Authority (Semanišin), the Slovak Republic (Semanišin), Šafárik University (Semanišin, Mihók, Vinar), Slovak Ministry of Finance (Semanišin), production control systems and mathematical simulation models for metallurgical production (Kyselovic), Internet/GSM Banking System in cooperation with the Industrial Bank of Košice (Mihók). They have also experience in participation in and management of international EC projects such as TEMPUS, COST, CEEPUS and several grants on national level. In addition to traditional programming languages from Pascal and C++ to HTML and Java they have extensive experience with such CASE tools as Westmount ISEE, Rational Rose, Excelerator and database systems such as Informix, DB2, Sybase, Paradox, Microsoft Access.
Vojtáš Peter, RNDr., doc., DrSc. (1951). Studied theoretical cybernetics at the Charles University in Prague (1974), PhD at Charles University, DrSc at the Computer Science Institute of the Czech Academy of Sciences, Associate Professor at Šafárik University, Košice and Research Director at the Mathematical Institute of the Slovak Academy of Sciences. Field of research: mathematical logic, fuzzy logic and their applications in computer science. 41 published papers, more than 100 citations, invited lectures at 12 international conferences, Humboldt Foundation Fellowship (Germany), visiting professor at Ohio University (USA). Head of Computer Science Dept., Faculty of Science, Šafárik U. of Košice, organizer and head of a team of (mostly) doctoral students active in the above field of research
[2] B.Balcar, P. Vojtas: Almost disjoint refinement of subsets of Bbb N,
Proc. Amer. Math. Soc., 79 (1980) 465-470.
[3] B. Balcar, P. Simon, P. Vojtas: Refinement properties and extending of filters, Bull. Acad. Polon. Sci., 28 (1980) 535-540.
[4] M. Gavalec, P. Vojtas:
Remarks to a modification of Ramsey type theorem, Comment. Math. Univ. Carolinae, 21
(1980) 727-738.
[5] B. Balcar, P. Simon, P. Vojtas: Disjoint refinement and related topics, Proceedings of the 8th Winter School on Abstract Analysis, Mathematical Institute, Czechoslovak Academy of Sciences, Prague, 1980, 16-25,
[6] P. Vojtas: Zjemnovacie systémy na booleovských algebrách, kandidátska dizertacná práca, Karlova Univerzita, Praha, 1980, 1-91.
[7] B. Balcar, P. Simon, P. Vojtas: Refinement properties and extensions of filters in
Boolean algebras, Trans. Amer. Math. Soc. 267 (1981) 265-283.
[8] P. Vojtas: A transfinite Boolean game and a generalization of Kripke's embedding theorem,
General Topology and its Relations to Modern Analysis and Algebra V,
Proc. 5th Prague Topological Symposium 1981,
J. Novák, Z. Frolí k eds., Helderman Verlag, Berlin, 1982, 663-668.
[9] P. Vojtas: Simultaneous strategies and Boolean games of uncountable length, Proc. 10th Winter School on Abstract Analysis 1982, Z. Froli k ed., Suppl. Rend. Circolo Mat. Palermo, Serie II, 1982, 293-297.
[10] P. Vojtas: Game properties of Boolean algebras, Comment. Math. Univ. Carolinae, 24 (1983) 349-369.
[11]
P. Vojtas:
Boolean games -- classifying strategies and omitting cardinality assumptions,
Proc. 11th Winter School on Abstract Analysis 1983, Z. Froli k ed.,
Suppl. Rend. Circolo Mat. Palermo, Serie II, 1984, 361-368.
[12]
R. Fric, P. Vojtas:
Convergent sequences in beta X,
Proc. 11th Winter School on Abstract Analysis 1983, Z. Froli k ed., Suppl. Rend. Circolo
Mat. Palermo, Serie II, 1984, 133-137.
[13]
E. Copl\'akov\'a, P. Vojtas:
A new sufficient condition for the existence of Q-points in
beta bb N - bb N, Topology and its Applications, Eger, Hungary, 1983,
Colloq. Math. Soc. Bolyai 41, North Holland, Amsterdam, 1985, 199-208.
[14]
R. Fri\v c, P. Vojtas:
Diagonal conditions in sequential convergence,
Proc. Convergence Structures, Bechyne, 1984, Math. Research 24, Akademie Verlag, Berlin,
1985, 77-94.
[15]
R. Fri\v c, P. Vojtas:
The space omega omega in sequential convergence,
Proc. Convergence Structures, Bechyne, 1984, Math. Research 24, Akademie Verlag, Berlin,
1985, 95-106.
[16]
P. Vojtas:
Set-theoretic characteristics of summability of sequences and convergence of series,
Comment. Math. Univ. Carolinae 28 (1987) 173-183.
[17]
P. Vojtas:
More on set-theoretic characteristics of summabilitiy of sequences
by regular (Toeplitz) matrices, Comment. Math. Univ. Carolinae 29 (1988) 97-102.
[18]
L. Spi\v siak, P. Vojtas:
Dependences between definitions of finiteness, Czech. Math. J. 38 (1988) 389-397.
[19]
P. Vojtas:
The strength of the comparison test versus gaps between convergent and divergent series,
General Topology and its Relations to Modern Analysis and Algebra VI,
Proc. 6th Prague Topological Symposium 1986, Helderman Verlag, Berlin, 1988, 617-622.
[20] P. Vojtas: Cardinalities of noncentered systems of subsets of bb N which reflect some qualities of ultrafilters, p-points and rapid filters, International Conference on Topology and its Applications, Baku, 1987, Math. Institute, Aserbaijan Acad. Sci., Baku, 1989, 263-268. (nedosiahnutelne, znovu opublikovane ako)
[20]
P. Vojtas:
Cardinalities of noncentered systems of subsets of omega, Discrete Math. 102 (1992)
125-129.
[21]
P. Vojtas:
A note on the effectiveness of tests for the absolute convergence
and divergence of infinite series, Math. Slovaca 42 (1992) 97-101.
[22]
P. Vojtas:
Topological cardinal invariants and the Galois-Tukey category,
Recent Developments of General Topology and its Applications,
W. Gahler, H. Herlich, G. Preuss eds., International Conference in Memory of Felix Hausdorff
(1868-1942), Mathematical Research 67, Akademie Verlag, Berlin, 1992, 309-314.
[23]
P. Vojtas:
Boolean isomorphism between partial orderings of convergent and divergent series and
infinite subsets of bb N, Proc. Amer. Math. Soc. 117 (1993) 235-242.
[24]
P. Vojtas:
Generalized Galois-Tukey connections between explicit relations on classical objects of
real analysis, Israel Math. Conf. Proc. 6 (1993) 619-643.
[25] P. Vojtas: Amoeba Relation and Galois-Tukey Connections, Acta Univ. Carolin. Math. Phys. 35 (1994) 67-74
[26] P. Vojtas: On omega * and absolutely divergent series, Topology Proceedings 19 (1994) 335-348.
[27] P. Vojtas: A lattice of binary relations with polarity, in Proc. Summer School on General Algebra and Ordered Sets, L. Jaan, Aug 29-Sep 5, 1993, dedicated to J. Jakubik, Ordered alg. structures '93, T. Katrinak, M. Ploscica, P. Zlatos eds., Tatra Mt. Math. Publ. 5 (1995) 143-150.
[28] P. Vojtas: Boolean universe versus fuzzy sets, R. Mesiar, V. Novák eds. Tatra Mt. Math. Publ. 6 (1995) 179-186.
[29] P. Vojtas, L. Paulík, M. Lieskovský. Expert systems and different fuzzy logic systems, in Proceedings of Artificial Intelligence Techniques '96, Brno, Czechia, J. Zizka and Brázdil eds., Technical University of Brno, 1995, 233-239.
[30] P. Vojtas, L. Paulík. Logic Programming in RPL and RQL, in Proceedings of SOFSEM '95, 22nd Seminar on Current Trends in Theory and Practice of Informatics, M. Bartosek, J. Staudek, J. Wiedermann eds., Lecture Note in Comp. Sci. 1012, Springer Verlag, 1995, 487-492.
[31] S. Krajci, P. Vojtas: On the Boolean structure generated by Q-points of omega *, Acta Univ. Carolin. Math. Phys. 36,2 (1995) 33-38.
[32] P. Vojtas, L. Paulík. Soundness and completeness of non-classical extended SLD-resolution, in Proc. ELP'96 Leipzig, ed. R. Dyckhoff et al., Lecture Notes in Comp. Sci. 1050 Springer Verlag, 1996, 289-301.
[33] P. Vojtas: Uncertain reasoning with floating connectives, in Proc. AIT'96 Brno, ed. J. Zizka, Technical University Brno, PC-Dir Publ. 1996, 31--40.
[34] P. Vojtas.Fuzzy reasoning with flexible selection of t-operators. In Proc. IFSA'97, M. Mares ed. Academia Praha 1997 345--350
[35] G. Andrejkova, P. Vojtas. Fuzzy Prolog with neural network connectives. In Proc. EUFIT'97, Publ. Verlag Mainz, Wissenschaftsverlag, Aachen, 1997, 57--61
[36] W. Just, P. Vojtas: On matrix rapid filters, Fund. Math. 154(1997)177--182
[37] P. Krisko, P. Marcincak, P. Mihok, J. Sabol, P. Vojtas. Low retrieval remote querying dialogue with fuzzy conceptual, syntactical and linguistical unification. In Flexible Querying Answering Systems 98, Roskilde, Denmark, T. Andreasen et al eds. Lecture Notes in Computer Science 1495, Springer Berlin 1998, 215--226
[38] P. Krisko, P. Marcincak, P. Mihok, P. Vojtas. Neurcitost pri spracovavani informacii. In Proc. Systems Integration 98, eds. J. Pour, J. Vorisek, University of Economics, Praha 1998,543--547
[39] P. Vojtas, J. Sabol. A decision support system based on fuzzy predicate logic abduction and remote querying. In Proc. Information Processing and Management under Uncertainty, ed. B. Bouchon-Meunier, Editions EDK Paris 1998, 1304--1309
[40] P. Vojtas: Series and Toeplitz matrices (a global/implicit approach), Tatra Mount. Math. Publ. 14 (1998) 269--281
[41] P. Vojtas. Tunable fuzzy logic programming for abduction under uncertainty. Workshop Many valued logic for AI applications. European conference on Artificial Intelligence 98, University of Brighton, 1998, 1--7
[42] P. Vojtas. Fuzzy reasoning with tunable t-operators. J. Advanced Comp. Intelligence 2 (1998) 121--127
[43] D. Smutna, P. Vojtas. Fuzzy resolution with residuation of material implication. In Proc. EUROFUSE-SIC'99, B. deBaets, J. Fodor, L. T. Koczy eds. TU Budapest, 1999, 472--476
[44] P. Mihok, K. Novakova, G. Semanisin, R. Sotak, J. Stoffova, P. Vojta s. Budovanie akademickeho informacneho systemu UPJS. In Zbornik medzinarodnej konferencie UNINFOS'99, ed. P. Mederly, Publ. MFF UK Bratislava, 1999, 110-115
[45] P. Vojta s. Fuzzy logic abduction. in Proc. of 1999 Eusflat-Estylf Joint Conference, G. Mayor, J. Suner eds. Universidad de les Illes Balears, Jorvich s.l. 1999, 319-322
[46] P. Vojtas. Translating boolean reals to fuzzy reals (reals and their topology), Tatra Mt. Math. Publ. 16 (1999) 255-268
[47] S. Fuchino, H. Mildenberger, S. Shelah, P. Vojtas. On absolutely divergent series. Fund Math. 160 (1999)255-268