From both terminals you have the same possibilities to come to the center. The most convenient way is offered by the Minibus-Service at very reasonable price. They take you to any address in Budapest with their comfortable 8-seaters, for 600 Forints (equivalent to 10 DM) per
************************************** * WE CAN STILL ACCEPT REGISTRATIONS! * ************************************** ************************************************************* > < > Third Announcement & Program of the Summer School < > < > ALGEBRAIC LOGIC and the METHODOLOGY OF APPLYING IT, < > < > July 11-17, 1994, Budapest, < > < > which is part of the TEMPUS Summer School series for < > Algebraic and Categorial Methods in Computer Science. < > < ************************************************************* This will be the third one in the above mentioned series of summer schools, attached to the TEMPUS project entitled "Algebraic and Categorial Methods in Computer Science". The summer school is sponsored by the European Community TEMPUS office. The summer school received support from IQSoft Budapest, too. ORGANIZING COMMITTEE: Hajnal Andreka, Miklos Ferenczi, Istvan Nemeti and Ildiko Sain ORGANIZING SECRETARY: Corinna Farkas ADDRESSES: Please send your correspondence to BOTH of the following two e-mail addresses: cora@ludens.elte.hu and h1468sai@ella.hu, or to the following mailing address: Ildiko Sain, Mathematical Institute, Budapest, Pf. 127, H-1364, Hungary. Fax: (36-1) 117-7166 (indicate: To Ildiko Sain). If you intend to participate, please, fill in & send back the REGISTRATION FORM attached to the end of this announcement (if you haven't done so yet). -------------------------------------------------------------------------- S C I E N T I F I C P R O G R A M Courses: ________________________________________________________________ | | | WILLEM BLOK and DON PIGOZZI: General Algebraic Logic | | | | VAUGHAN PRATT: Chu Spaces: Complementarity and Uncertainty in | | Rational Mechanics | | | | YDE VENEMA: Boolean Algebras with Operators & Modal Logic | | | | ISTVAN NEMETI and HAJNAL ANDREKA: Algebras of Relations of | | Various Ranks & their Applications | | | | WORKSHOP GIVEN BY YOUNG RESEARCHERS: Decidability issues and | | logics related to the dynamic trend | | | | UNIVERSAL ALGEBRA TUTORIAL | |________________________________________________________________| Talk: ANTONINO SALIBRA (joint work with Don Pigozzi): The Abstract Variable-binding Calculus ABSTRACTS OF COURSES: Willem Blok and Don Pigozzi: GENERAL ALGEBRAIC LOGIC "General algebraic logic" can be characterized as the process of reducing logical deduction, in its broadest sense, to equational logic, the particularly simple form of logical deduction that underlies most of modern algebra. In these lectures we investigate the precise method by which this reduction can be either completely or partially effected. We show how this leads to close connections between logical systems and suitable classes of algebras, enriched with a predicate when the reduction is only partial. We outline the theory of algebraization in a very general context, illustrating the ideas with numerous examples. Having isolated a precise notion of algebraizable logic, we show how it provides the proper framework for studying algebraic equivalents of metalogical properties as, for example, the property of "possessing a deduction theorem". --------------- Vaughan Pratt: CHU SPACES: COMPLEMENTARITY AND UNCERTAINTY IN RATIONAL MECHANICS "Rational mechanics" captures mind-body duality for autonomous agents in essentially the same way that quantum mechanics captures momentum-position duality for physical systems, with Chu spaces in place of Hilbert spaces. Chu spaces expose a Heisenberg-like uncertainty principle as a previously unnoticed yet prominent feature of Stone duality. --------------- Yde Venema: BOOLEAN ALGEBRAS WITH OPERATORS & MODAL LOGIC Formalisms related to Modal Logic play an important role in theoretical computer science: think of examples like epistemic logic, dynamic logic or relational algebra. Such formalisms can be treated in a nice algebraic way via the theory of Boolean Algebras with Operators (BAO's). The course will be centered around two themes: (1) the duality between BAO's and Relational (Kripke) Structures, and (2) modal/algebraic languages to describe these structures. We will review some important and elegant theorems, like automatic completeness results for a large class of logics. --------------- Istvan Nemeti and Hajnal Andreka: ALGEBRAS OF RELATIONS OF VARIOUS RANKS & THEIR APPLICATIONS Theories of relations (binary ones, ternary relations, n-ary ones etc.) play an essential role both in Computer Science and in Logic. Besides quantifier logics, they are important for e.g. logics of the dynamic trend, resource-sensitive logics, substructural logics, logics of actions etc. We will study algebras whose elements are relations. Research in this area has been going on for 140 years, hence its theory is powerful and profoundly applicable. The goal of the course is to make this rich theory accessible, to provide insight into why and how it works, and to highlight the main directions in which it is "moving". --------------- Agnes Kurucz and Ildiko Sain: UNIVERSAL ALGEBRA TUTORIAL Algebras, subalgebras, homomorphisms, congruences, Cartesian products. Subdirect decomposition, simple and subdirectly irreducible algebras. Birkhoff's subdirect decomposition theorem. Ultraproducts, Los theorem. Birkhoff's variety characterization theorem, quasi-variety characterization theorem. Discriminator varieties. We will give only a brief survey of the above broad material, concentrating on theorems frequently used in algebraic logic. Theorems will be stated and explained but usually not proved. A detailed lecture notes containing full proofs will accompany the lectures. --------------- ABSTRACT OF TALK: Antonino Salibra (joint work with Don Pigozzi): THE ABSTRACT VARIABLE-BINDING CALCULUS In this talk we illustrate how the algebraizations of classical and nonclassical logics fit into a general framework of variable-binding and variable-substitution that includes such diverse variable-binding operations as lambda abstraction, definite Riemann integration, universal and existential quantification (in both classical and intuitionistic logic), and various notions of generalized quantification. The main conceptual devices used are the abstract variable-binding calculus (VB-calculus) and the variety of polyadic VB-algebras. We show that every locally finite polyadic VB-algebra is isomorphic to a functional polyadic VB-algebra that is obtained from some model of the VB-calculus by a natural coordinatization process. As an application of this result, we present a strong completeness theorem for the VB-calculus that specializes to give a completeness theorem for every VB-theory. In particular, this result specializes to a completeness theorem for the familiar formal systems above specified. --------------- ABSTRACTS OF WORKSHOP LECTURES: Viktor Gyuris: FINITE SCHEMA AXIOMATIZABLE ALGEBRAIZATION OF FIRST-ORDER LOGIC The algebraic counterparts of first-order logic obtained so far (e.g. representable cylindric algebras, representable polyadic algebras, representable relation algebras) are not axiomatizable even with a finite schema of equations. This negative property has lead to serious difficulties of various kinds. Here we present an algebraic counterpart of first-order logic which is axiomatizable by a simple finite schema of equations. The key step is to choose the operations suitably on algebras whose elements are relations of higher ranks. --------------- Agnes Kurucz: DECIDABLE & UNDECIDABLE VARIETIES OF BAO'S AND LOGICS TOUCHED BY THE DYNAMIC TREND We shall map the landscape of logics of the so called dynamic paradigm from the point of view of decidability and undecidability. We will see what this "map" means for decidability issues about the equational theories of the algebraic counterparts of these logics. As a byproduct, we will get a "systematic" answer to the question "Which varieties of Boolean algebras with operators are decidable?". Proof methods will be discussed, too. --------------- Maarten Marx: ARROW LOGICS: A PARADIGM FOR LOGICS TOUCHED BY THE DYNAMIC TREND Research in areas such as Computer Science, Linguistics, Artificial Intelligence and Cognitive Science gave birth to a new paradigm for doing logic which for brevity we will call the dynamic paradigm. Logics of this paradigm include dynamic logic, action logic(s), dynamic semantics, resource sensitive logics such as linear logic and its fragments and Lambek Calculus, process logics and algebras, various temporal logics etc. The theory of Arrow Logics is both (i) the common backbone of all these new logics, and (ii) an explicit formulation of the new paradigm. One of the purposes of Arrow Logic is to give insight into the common essence of all these logics or, in other words, into "what makes them tick". --------------- Szabolcs Mikulas: A TECHNOLOGY FOR OBTAINING WELL-BEHAVED & STRONG ALGEBRA OF RELATIONS There are many well-investigated and useful logics that do not behave nicely in certain respects. Such examples are the undecidability of classical first-order logic, FOL, incompleteness of its finite variable fragment, Ln, and the incompleteness and undecidability of the strongest versions of logics of dynamics and action or resource sensitive logics etc. Following the ideas of van Benthem and Nemeti, we will discuss how to "tame" logics so that they behave in a nice way, and at the same time, remain strong (expressive) or become even stronger. That is, using the powerful methods of algebraic logic, we will reformulate several logics and show that these new versions (i) have desirable properties such as completeness, decidability etc., and at the same time (ii) their expressive powers remain great or become even greater. --------------- Szabolcs Mikulas and Andras Simon: METHODOLOGY OF APPLYING ALGEBRAIC LOGIC TO LOGIC This talk aims at improving understandability and usefulness of the Andreka-Nemeti (AN) lectures as well as the rest of the workshop lectures. The algebraic investigations in the AN lectures are applied in the workshop talks, among others, to logics originating from computer science, linguistics, cognitive science. The present talk explains the methodology of these and other applications, putting both the AN lectures and the workshops in perspective. We present a methodology of translating purely logical problems to algebra, then solving them by the strong machinery available in algebra, and then translating the result back to logic. The AN lectures as well as the workshops will occasionally refer to the material covered in the present talk. --------------- A TENTATIVE schedule of the programme is in the chart below. Abbreviations: UA tuto = Universal Algebra Tutorial A-N = Andreka-Nemeti B-P = Blok-Pigozzi M-S = Mikulas-Simon W = Workshop +---------+---------+---------+---------+---------+---------+ | Monday | Tuesday |Wednesday|Thursday | Friday |Saturday | |=======|=========|=========|=========|=========|=========|=========| | 8- 9 | | UA tuto | | | | | |-------|---------|---------|----W----|---------|----W----|----W----| | 9-10 | Pratt | UA tuto | M-S | Pratt | Mikulas | M-S | |-------|---------|---------|---------|---------|---------|----|----| | 10-11 | Pratt | B-P | Pratt | B-P | B-P |A-N |Ven.| cons. |-------|---------|---------|---------|---------|---------|----|----| | 11-12 | UA tuto | B-P | Pratt | B-P | B-P |B-P | | cons. |-------|---------|---------|---------|---------|---------|----|----| | 12-13 | | | | | | | |-------|---------|---------|---------|---------|---------|---------| | 13-14 | | | | | | | |-------|---------|---------|---------|---------|---------|---------| | 14-15 | A-N | Venema | A-N | Venema | A-N | E | |-------|---------|---------|---------|---------|---------|---------| | 15-16 | A-N | Venema | A-N | Venema | Venema | X | |-------|---------|---------|---------|---------|---------|---------| | 16-17 | | Salibra | Marx | Kurucz | Gyuris | C | |-------|---------|---------|----W----|----W----|----W----|---------| | 17-18 | | | | | | U | |-------|---------|---------|---------|---------|---------|---------| | 18-19 | | | | | | R | |-------|---------|---------|---------|---------|---------|---------| | 19-20 | party | | | | | S | |-------|---------|---------|---------|---------|---------|---------| | 20-21 | party | | | | | ION | +-------+---------+---------+---------+---------+---------+---------+ LECTURE NOTES: Every registered participant will receive basic lecture notes for courses indicated in the program. Besides these notes, scientific papers for further reading and extra copies of the lecture notes will be sold throughout the summer school. --------------------------------------------------------------------------- G E N E R A L I N F O R M A T I O N ACCOMMODATION: In double bedrooms for 14 DM/day, or in single bedrooms for 18 DM/day, in Summer Hotel Hill. The lectures will be in the same building. Address: Budapest, district XI, Menesi street 5. MEALS: Continental breakfast for 4 DM/day, lunch for 5,3 DM/day in Summer Hotel Hill. The Drink Bar of Summer Hotel Hill is open from 7 a.m. until late at night. Many restaurants are available in the neighborhood of Summer Hotel Hill. REGISTRATION: All participants are requested to register and to pay the conference fee and charges as appropriate, at the Reception Desk on Sunday, July 10: 6 p.m. - 10 p.m. or on Monday, July 11: 8 a.m. - 9 a.m. or 12 a.m. - 14 p.m. or 16 p.m. - 18 p.m. The Reception Desk is located close to the entrance of Summer Hotel Hill. REGISTRATION FEE: 120 DM for participants 50 DM for accompanying persons. EXCHANGE OF CURRENCY: Foreign currency can be brought into Hungary without restriction and there is no obligation for exchanging currency. However, in general, you have to use Hungarian currency (HUF called Forints in Hungarian) in shops. Exchange bureaux are available at the airport, in bigger hotels, in banks and other places. TRAVEL: Budapest has two airport terminals, Ferihegy I and Ferihegy II. person. Tickets are available at the Airport passenger service counters. You can also choose to use buses called "Centrum Airport Service" as well. These buses leave every 30 minutes to Erzsebet square in central Budapest for 200 Forints (equivalent to 3,3 DM), from where you can take tram no.49 or no.47 to "Moricz Zsigmond korter", the nearest square to your accommodation (Summer Hotel Hill, Menesi street 5), which is at 5 minutes walking distance from the tram station at Moricz Zsigmond korter. For using public transportation in Budapest (trams, buses, Metro or trolley buses), tickets must be purchased in advance, for 25 Forints (0.5 DM) each trip. One can buy tickets from slot machines (there are some slot machines at the airport terminal bus stations), at Metro stations, or from some of the small shops selling newspaper or tobacco. Taxi from Ferihegy to central Budapest costs about 2000 Forints (equivalent to 33 DM). From Nyugati palyaudvar (Western Railway Station) you can reach Moricz Zsigmond korter by tram no.4 or no.6. From Keleti palyaudvar (Eastern Railway Station) to Moricz Zsigmond korter take bus no.7 or no.red 7, from Deli palyaudvar (Southern Railway Station) tram no.61. RENT A CAR: This service is at your disposal at Ferihegy Airport and all larger hotels. We can offer leaflets on them. SPORT FACILITIES in the Summer Hotel Hill: 25m swimming pool and sauna will be open from Monday to Friday: 6 a.m. - 9 p.m., during weekend: 8 a.m. - 6 p.m. One ticket costs 220 HUF, a ticket for 6 occasions (usable once a day) costs 600 HUF. Tickets can be bought at the reception of Summer Hotel Hill. The rent of the Fitness room is 120 HUF for one hour. The rent of the Drill Hall is 2200 HUF for one hour; here you can play tennis, basketball, volley ball, football. You have to take care of rackets and balls yourself. SOCIAL PROGRAMS: Reception on Monday evening and an excursion on Saturday afternoon. See also "Final notes" below. BOOK FAIR: From Tuesday (12th of June) to Thursday (14th) there will be a display and fair of books relevant to the Summer School, by Springer-Verlag and perhaps by Oxford University Press as well. MUSEUMS: Most museums are open from 10 a.m. to 6 p.m. All museums are closed on Monday. SHOPPING HOURS: Shopping hours are generally 10 a.m. to 6 p.m. on weekdays. On Saturday the majority of shops are closed, the rest close early afternoon. In shops you have to use Hungarian currency. (There are some exceptional places where foreign currency is accepted.) WEATHER: Hungary has a continental climate. The weather in July is generally dry and warm, with average temperatures between 24 and 30 centigrade. ---------------------------------------------------------------------- We hope this small map will help you to find Summer Hotel Hill in Budapest: / st. / / / 1: Bus stop no.7 from center | | | ************** / B. / 2: Bus stop no.7 to the center | | | |Summer Hotel| | / / 3: Tram stop no.4 and 6 ____| |_| |___Hill_____| | / k / 4: Tram stop no.47 to the center ____ __ Menesi st.___ \ / o / 5: Tram stop no.47 from center |H| \ \/ t / 6: Tram stop no.49 to the center |i| \ r / |m| / a / 2 This big crossing is called: |f| _/ B /______ "Moricz Zsigmond korter" ____|y|_______________/ _____ \____________________ _ / \ Villanyi st. /1/ 6 / Park | Karinthy Frigyes st. ___________________/_/ / 4/ ___________________ | /_______ / | / ____5__ / 3 / / \ Feher| / / | vari | | sreet| --------------------------------------------------------------------------