# LIBOR BĚHOUNEK: VÝROKOVÁ FUZZY LOGIKA OTÁZEK

(This is the syllabus of my talk at 8th VlaPoLo, Zielona Gora, on a similar topic.)

The many-valued approach to erotetic logic is one of the most important generalizations of its classical variants. Its value for applications is shown, i.a., by the fact that many questionnaires use scaled answers rather than simple yes-no ones. A specific branch of many-valued logic is fuzzy logic, which is aimed at capturing the notion of vagueness and degrees of truth. Recent advances in metamathematics of fuzzy logic ([1], [2]) made it possible to generalize various branches of mathematics and logic so as to deal with vagueness and uncertainty.

Fuzzy logic takes the set of truth-values (degrees of truth) to be the real interval [0,1]. T-norm based fuzzy logic starts from a few natural assumptions about the truth function representing conjunction: commutativity, associativity, continuity, monotonicity, and classical values for classical arguments. These conditions lead to Hajek’s Basic Fuzzy Logic BL with its important extensions, incl. Goedel and Lukasiewicz infinite-valued logics.

Groenendijk-Stokhof erotetic logic (GS) is an intensional system based on the notion of logical space ([3], [4]). The intension of a declarative sentence is a subset of the logical space; questions are identified with partitions of the logical space. The notions of answerhood and entailment for questions are defined by means of the intensions of the answers and the blocks of the partition.

In the talk, I shall sketch the generalization of GS to fuzzy setting. Starting with fuzzy intensional semantics for propositions (the intension of a proposition is a fuzzy subset of the logical space), I proceed to definitions of fuzzy questions and fuzzy answerhood, entailment and equivalence conditions. I discuss various options for the definitions and show their respective motivation and mutual relationship. Finally, I try to assess the prospects of fuzzified GS in both theory and applications.

References

[1] Hajek, Petr: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht 1998.
[2] Hajek, Petr and Godo, Lluis: Deductive systems of fuzzy logic. Tatra Mountains Math. Publ. 13 (1997), 35-66.
[3] Groenendijk, Jeroen and Stokhof, Martin: Questions. In: van Benthem and ter Meulen (eds.), Handbook of Logic and Language, Elsevier/MIT 1994.
[4] Groenendijk, Jeroen and Stokhof, Martin: Partitioning Logical Space. 2nd ESSLLI Annotated Handout, Leuven 1990.