HOSTÉ – ZVANÉ PŘEDNÁŠKY:

MARTIN KUSCH: WITTGESTEIN, METROLOGY, CERTAINTIES

(Institute of Philosophy, October 4, 2012)

CHRISTOPHER GAUKER: VALIDITY WITHOUT REFERENCE

(Institute of Philosophy, February 20, 2012)

GEORG BRUN: LOGICAL SYSTEMS, REFLECTIVE EQUILIBRIUM AND LOGICAL PLURALISM

(Institute of Philosophy, December 12, 2011)

HERBERT HRACHOVEC: LOGIC OF PARMENIDES

(Institute of Philosophy, April 18, 2011)

MARK VAN ATTEN: KANT AND REAL NUMBERS

(Institute of Philosophy, March 28, 2011)

MARTIN KANOVSKÝ: VÝZNAM A REPREZENTACE

(Institute of Philosophy, March 21, 2011)

GARY KEMP: LATER WITTGENSTEIN ABOUT THE UNITY OF PROPOSITION

(Institute of Philosophy, December 6, 2010)

TIMM LAMPERT: WHY IS IT IMPOSSIBLE TO DIVIDE A NUMBER BY 0?

(Institute of Philosophy, November 29, 2010)

PAVOL ZLATOŠ: GÖDELOV ONTOLOGICKÝ DÔKAZ EXISTENCIE BOHA

(Institute of Philosophy, November 22, 2010)

MILOŠ TALIGA: NAČO JE DOBRÝ SOCIÁLNY OBRAT V EPISTEMOLÓGII?

(Institute of Philosophy, November 1, 2010)

FRANTIŠEK GAHÉR: SPORY O STOICKÚ LOGIKU

(Institute of Philosophy, March 22, 2010)

CARLES NOGUERA: GENERAL THEORY OF LOGICS WITH IMPLICATION II

(Institute of Computer Science ASCR, November 18, 2009)

CARLES NOGUERA: GENERAL THEORY OF LOGICS WITH IMPLICATION I

(Institute of Computer Science ASCR, November 11, 2009)

GABRIEL SANDU: BETWEEN TRUTH AND PROOF

(Department of Logic and Institute of Philosophy, October 5, 2009)

COLIN CHEYNE: EMOTION, FICTION AND RATIONALITY

(Institute of Philosophy, September 17, 2009)

MARIÁN ZOUHAR: VŠEOBECNÉ TERMÍNY A ICH RIGIDNOSŤ

(Department of Logic and Institute of Philosophy, May 14, 2007)

GABOR KUTROVATZ (BUDAPEST): SCIENCE STUDIES – SCIENCE WARS

(Department of Logic and Institute of Philosophy, April 23, 2007)

GABRIEL SANDU: NOTIONS OF DEPENDENCE AND INDEPENDENCE IN GTS

(Department of Logic and Institute of Philosophy, April 16, 2007)

GOTTFRIED GABRIEL: FREGE ALS PHILOSOPH – ZUM VERHÄLTNIS VON ERKENNTNISTHEORIE, LOGIK UND SPRACHPHILOSOPHIE

(Department of Logic and Institute of Philosophy, March 19, 2007)

GILLMAN PAYETTE: LOGICAL PLURALISM: FACT OR FICTION

(Department of Logic and Institute of Philosophy, March 12, 2007)

HANS ROTT: BELIEF CHANGE AND FREE WILL

(Department of Logic and Institute of Philosophy, March 5, 2007)

DAVID MAKINSON: LOGIC AND PROBABILITY: AN UNEASY PARTNERSHIP

(Department of Logic and Institute of Philosophy, December 11, 2006)

LADISLAV KVASZ: O VZTAHU VIZUÁLNYCH A SYMBOLICKÝCH REPREZENTÁCIÍ V MATEMATIKE

(Department of Logic, November 27, 2006)

SIMO RINKINEN: DEFLATIONISM AND GÖDELˈS THEOREMS

(Department of Logic and Institute of Philosophy, December 4, 2006)

TIM CRANE: NON-EXISTENT OBJECTS

(Department of Logic and Institute of Philosophy, November 27, 2006)

PATRICK GREENOUGH

(Uncertainity: Reasoning about probability and vagueness, September 5-8, 2006, Villa Lanna, Prague)

The Open Future

The goal in this talk is to delineate two closely related models of the open future. The first of these is a truthmaker gap model, the second is a truthmaking gap model. These models share the following features: (1) They are both branching-time models of the open future. (2) However, they pose no threat to classical logic or classical semantics and they thus stand in contrast to the many and various enduringly popular truth-value gap conceptions of the open future. (3) They both deploy conceptions of indeterminacy which are able to capture the hitherto elusive (non-epistemic) distinction between truth and determinate truth. (4) As a result, they stand in opposition to what may be termed the orthodox conception of (worldly) indeterminacy. (5) They allow that determinate truth and indeterminate truth (for token utterances) are both absolute. (6) Despite the fact that time branches, the (indexical) singular term `The futureˈ refers to one and only one of these future histories-though at the time of utterance it is not determined which one. (7) In consequence, the conceptions on offer do not threaten eternalism since the past, the present, and the future all exist (though they are not all equally real). (8) Moreover, unlike all other extant branching conceptions of time, both models yield a perfectly natural specification of the truth-conditions of a future-tensed sentence in terms of what happens in the future with respect to the utterance of the sentence in question. (9) Though both models are developed within a static conception of time (under which time has a B-ordering) they are also compatible (when suitably adjusted) with a dynamical conception (under which time has an A-ordering). (10)Finally, they are available to both deflationary and inflationary conceptions of truth, truthmakers, and truthmaking.

PETER MILNE

(Uncertainity: Reasoning about probability and vagueness, September 5-8, 2006, Villa Lanna, Prague)

Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events

Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation space presents an especially tractable case to help get one’s bearings. Two solutions present themselves: the first takes as upper and lower probabilities of the event X the (exact) probabilities assigned X’s upper and lower rough-set approximations; the second, motivated both by formal considerations and by a simple betting argument, is to treat X’s rough-set approximation as a conditional event and assign to it a point-valued (conditional) probability. With rough sets over an approximation space we get a lot of good behaviour. For example, in the first construction mentioned the lower probabilities are 2-monotone. When we examine other models of approximation/imprecision/vagueness, and in particular, proximity spaces, we lose a lot of that good behaviour. In the literature there is not (even) agreement on the definition of upper and lower approximations for events (subsets) in the underlying domain. Betting considerations suggest one choice and, again, ways to assign upper and lower and point-valued probabilities.

HEINRICH WANSING

(Department of Logic and Institute of Philosophy, May 15, 2006) Abstract

WOLFGANG KIENZLER

(Department of Logic and Institute of Philosophy, April 3, 2006

Institute of Philosophy, May 11, 2006)

Frege on Numbers, Concepts, and Objects (1884-1893)

In order to eventually derive arithmetic from logic Frege in 1879 introduced his logical notation, taking the function-argument-form f(x) as his fundamental logical relation (logische Grundbeziehung). In his later work he developed the implications of this decision. Frege was led to sharply and absolutely distinguish concepts from objects (in Grundlagen der Arithmetik), and this made it very difficult for him to introduce numbers because they combine features of concepts (they can be ordered a priori and systematically) with features of objects (they show individuality). Frege then undertook several attepts to pass from statements about concepts to statements about objects, with extensions of concepts intended to serve as something in-between. Fregeˈs notorious remarks about the concept horse also are to be evaluated in the light of these attempts. After Frege failed to bridge the gap between concepts and objects he hesitatingly introduced Basic Law V as a technical device, but this immediately led to the contradiction of classes. Thus the concept-object-distinction is at the same time essential for Fregeˈs sucess in logic and for his misfortune in his work on the foundations of arithmetic.

Wittgensteinˈs Remarks on Gödel

Wittgensteinˈs remarks on Gödel in his Remarks on the Foundations of Mathematics, Part I. Appendix III have been widely criticized, less often defended but most of all their point and scope has been almost totally misunderstood. Some essential features have to be noted:

Wittgenstein deliberately puts aside his (testified) knowledge of the (first incompleteness) theorem and any of its details. For his own purposes he presupposes its correctness.

Wittgenstein only discusses the claims, put forward by Gödel himself and others, as to the results and meaning of the theorem. This he does patiently and in much detail.

Wittgenstein compares the statement There are true but unprovable propositions in mathematics with the most basic constitution of mathematics. His investigation puts the very intelligibility of this statement into question (not its supposed truth).

Following Wittgensteinˈs analysis we can ask: How can a mathematical theorem start from a certain conceptual framework and end up in apparently overthrowing this very framework?

Wittgenstein shows through his reiterated attempts in his remarks on Gödel: if we stick to our initial conceptual framework throughout a series of proofs we conduct, then we never reach a situation where we would seriously state: Yes, now we have come across a true but unprovable proposition – where true and unprovable apply to the same mathematical system.

Eventually Wittgenstein points out important similarities between Gödelˈs theorem and the logical contradictions. He would be happy to agree that here we have the opposite of a contradiction (Gödel), for this would again be a contradiction.

It seems curious that Wittgensteinˈs remarks have attracted such fierce attacks when they are really only about the (non-rigorous) prose part. However, this fact gives rise to the suspicion that much more of the discussion about Gödelˈs (first incompleteness) theorem is dependent on these prose remarks than is usually admitted. In this way, Wittgensteinˈs remarks, precisely through their by-passing any formal questions, address the conceptual confusion at the heart of those extendes discussions.

CARLES NOGUERA I CLOFENT: ON N-CONTRACTIVE FUZZY LOGICS

(Institute of Computer Science, October 12, 2005) Abstract

JOOST J. JOOSTEN: PROVABILITY, INTERPRETABILITY AND PROOF STRENGTH

(Logic Seminar, Mathematical Institute, May 16, 2005)

BJORN JESPERSEN: MALFUNCTION AND MODIFICATION

Is a broken corkscrew a corkscrew? In general, if x is a malfunctioning F-device, is x then an F-device? The proper-function theorist says Yes, for the proper function of x as an F overrides its malfunctioning as an F. The pragmatist says No, for nothing that fails to function as an F is an F, while anything that does function as an F is an F. I favour an answer in the affirmative, basically because x was designed to function as an F-device. This is not to say, though, that everything that is designed to function as an F is an F. A plan for designing F-devices may be structurally flawed in such a way that nothing manufactured in accordance with it could possibly function as an F-device and, therefore, would not be an F. Our intuitions as to what makes x an F in the first place will strongly influence our intuitions concerning malfunction.

The purpose of my talk is to outline a logical system within which to reason about malfunction. I am going to address the following three issues.

formation of the property denoted by the predicate ‘is a malfunctioning F’

predication of ‘is a malfunctioning F’ of individual technical artifacts

validity, or invalidity, of various arguments in which the predicate ‘is a malfunctioning F’ occurs.

By arguing that a broken corkscrew is still a corkscrew, I have argued that the predicate modifier ‘malfunctioning’ is subsective [roughly, FG(x) / G(x)], hence not privative [roughly, FG(x) / not G(x)]. However, since ‘malfunctioning’, as it occurs in ‘is a malfunctioning F’, is a modifier, it cannot be intersective [roughly, FG(x) / F(x) et G(x)]. Still, we can infer that a broken corkscrew is broken, thanks to the rule of pseudo-detachment, so that we obtain something equivalent to the first conjunct of F(x) et G(x). The rule says, roughly: FG(x) / *F(x). In words, “a malfunctioning F malfunctions”. The idea behind the rule is to convert an attributive occurrence of ‘malfunctioning’, e.g., ‘F’, into a predicative occurrence, ‘F*’. The rule of pseudo-detachment has been developed together with Pavel Materna and Marie Duží. It forms part of a general project on intensional logic, which is in this case applied to properties and the phenomenon of predicate modification.

TERO TULENHEIMO: IF LOGIC

AHTI PIETARINEN: TOWARDS THE HISTORY OF LOGIC & GAMES

Prague International Colloquium, Logic: Logic, Games, and Philoophy (September 28 – October 1, 2004)

Ahti Pietarinen – Abstract

This talk traces the joint roots of logical and game-theoretic developments, starting from the late medieval obligationes, wandering through the central ideas of pragmatism, and ending at the mid-50s Princeton campus, the formal nexus of these mutual developments. This excursus shows that logic and games, mutually conceived, are an old but diversiform intellectual idea, the characteristics of which we are only gradually beginning to appreciate.

RONNY MELZ: SEMANTIC TALK AND THEORETICAL APPROACHES TOWARDS STATISTICAL PROPERTIES OF LANGUAGE AND CONCEPTUAL GRAPHS

I will present the model for a possible source of language, i.e. associative semantic networks. They are evidenced from the background of cognitive science and psychology [1, 2, 6] and seem to occur in a variety of real-life networks. The most significant properties distinguishing them from mere random graphs are the scale-free and the small-world structure [1] which directly relates to statistical properties of the graph representation [4]. However, when being mapped into fluent speech, the network structure is being folded to match into the linear channel described best by [5] and statistical properties thereof by [6]. With Semantic Talk [7] we try to, say, reverse-engineer the language stream to yield the original structure – not the conceptual network of a specified person, but rather a common groundwork reflected by the Wortschatz-corpus. Semantic Talk involves three main stages: the analyses of a spoken language stream extracting the main ideas, semantic information retrieval from the Wortschatz-database, and presentation of the most significant related concepts on the screen. To approach the last step, a graph drawing algorithm based on a force-directed vertex model has been implemented. As always in IR, no perfect match can be guaranteed. Nevertheless, due to its real-time capability, the software has a wide range of applications: in meetings, explicit semantic contexts are an invaluable help to progress or delve into new ideas, to provide a moderating assistance function to isolate problems and approach them from different points of view, or lastly to depict conceptual relations among conference papers in terms of a graph, e.g.

[1] Steyvers and Tenenbaum (in press): The Large-Scale Structure of Semantic Networks, Stanford University

[2] John F. Sowa (1984): Conceptual Structures – Information Processing in Mind and Machine, Addison-Wesley, Reading Massachusetts

[4] Farkas, Derény, Barabási, Vicsek (2001): Spectra of „Real-World“ Graphs: Beyond the Semi-Circle Law, Physical Review E 63, 026704

[5] Claude E. Shannon (1948): A Mathematical Theory of Communication, The Bell Systems Technical Journal, Vol. 27

[6] George K. Zipf (1965): Human Behavior and the Principle of Least Effort, Addison-Wesley Press.

[7] Biemann, Böhm, Heyer, Melz (2004): Automatically Building Concept Structures and Displaying Concept Trails for the Use in Brainstorming Sessions and Content Management Systems, Proceedings of I2CS, Guadalajara, Mexico and Springer LNCS

SUSANA MUÑOZ HERNÁNDEZ: FUZZY PROLOG

Ostrava, Research Laboratory of Intelligent Systems (LABIS), Friday, October 8, 2004, 13:00, Room No. A320.

Abstract

Incomplete information is a problem in many aspects of actual environments. Furthermore, in many scenarios the knowledge is not represented in a crisp way. It is common to find fuzzy concepts or problems with some level of uncertainty. Nowadays it is difficult to find practical systems that handle fuzziness and uncertainty. The few examples that we can find are minoritaries. To extend a popular system (which many of programmers are using), Prolog, with the ability of combining crisp and fuzzy knowledge representations seems to be an interesting issue.

We use default knowledge to combine the Closed World Assumption (CWA) and the Open World Assumption (OWA) to represent uncertainty in Logic Programming. This new framework is used to enhance Fuzzy Prolog [1] (for example by combining crisp and fuzzy logic in Prolog programs). Fuzzy Prolog is a language that models B([0; 1])-valued Fuzzy Logic. It subsumes former approaches because it is more general in two aspects: it uses a truth value representation based on unions of sub-intervals on [0,1] (Borel algebra) and it is defined using general operators (instead of a fixed one) that can model different logics.

Declarative and procedural semantics for Fuzzy Logic programs were defined and shown equivalent in [1]. This fuzzy extension to Prolog was realized by incorporating fuzzy reasoning into a set of constraints which are propagated through the rules by means of aggregation operators. An interpreter for this language using Constraint Logic Programming over Real numbers (CLP(R)) has been implemented and is available in the Ciao system [2]. The incorporation of default reasoning in Fuzzy Prolog removes some de ciencies inherited from Prolog and requires a richer semantics, which we discuss.

In the talk I will describe the Fuzzy Prolog approach, I will give an intuition about its semantics and I will provide some interesting details related to its implementation.

Keywords: Fuzzy Prolog, Modeling Uncertainty, Logic Programming, Constraint Programming Application, Implementation of Fuzzy Prolog.

References

[1] S. Guadarrama, S. Muñoz, and C. Vaucheret. Fuzzy prolog: A new approach using soft constraints propagation. Fuzzy Sets and Systems, FSS, 144(1):127{150, 2004. ISSN 0165-0114.

[2] M. Hermenegildo, F. Bueno, D. Cabeza, M. Carro, M. García de la Banda, P. López- García, and G. Puebla. The CIAO Multi-Dialect Compiler and System: An Experimentation Workbench for Future (C)LP Systems. In Parallelism and Imple- mentation of Logic and Constraint Logic Programming, pages 65{85. Nova Science, Commack, NY, USA, April 1999.

OLIVER KRUG: ON EMPTY SINGULAR TERMS

(Seminář 24. 4. 2004, soustředění v Peci p. Sn.)