Abstract
The article presents several adaptive fuzzy hedge logics. These logics are designed to perform a specific kind of hedge detection. Given a premise set Γ that represents a series of communicated statements, the logics can check whether some predicate occurring in Γ may be interpreted as being (implicitly) hedged by technically, strictly speaking or loosely speaking, or simply non-hedged. The logics take into account both the logical constraints of the premise set as well as conceptual information concerning the meaning of potentially hedged predicates (stored in the memory of the interpreter in question). The proof theory of the logics is non-monotonic in order to enable the logics to deal with possible non-monotonic interpretation dynamics (this is illustrated by means of several concrete proofs). All the adaptive fuzzy hedge logics are also sound and strongly complete with respect to their [0,1]-semantics.
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References
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., & Patel-Schneider, P. (Eds.). (2003). The description logic handbook: Theory, implementation and applications. Cambridge: University Press.
Barsalou, L. W. & Hale, C. R. (1993). Components of Conceptual Representation: From feature Lists to Recursive Frames. In I. Van Mechelen, J. Hampton, R. Michalski, & Theuns, P. (Eds.), Categories and concepts: Theoretical views and inductive data analysis (pp. 97–144). San Diego, CA: Academic Press.
Barsalou, L. W. (1982). Context-independent and Context-dependent Information in Concepts. Memory and Cognition 10, 82–93.
Batens, D. (2007). A universal logic approach to adaptive logics. Logica Universalis, 1, 221–242
Batens, D. (2004). The need for adaptive logics in epistemology. In D. Gabbay, S. Rahman, J. Symons, & J. P. Van Bendegem, (Eds.), Logic, epistemology and the unity of science (pp. 459–485). Dordrecht: Kluwer.
Costello, F. J. & Keane, M. T. (2000). Efficient creativity: constraint guided conceptual combination. Cognitive Science, 24, 299–349.
Conrad, C. (1972). Cognitive economy in semantic memory. Journal of Experimental Psychology, 92, 149–154.
Esteva, F., Godo, L., Hájek, P., & Navara, M. (2000). Residuated fuzzy logics with an involutive negation. Archieve for Mathematical Logic, 39, 103–124.
Grice, P. (1989). Studies in the way of words. Cambridge, Massachusetts: Harvard University Press.
Hájek, P. (2000). Metamathematics of fuzzy logic. Dordrecht: Kluwer.
Hájek, P. & Harmankova, D. (2000). A hedge for Gödel fuzzy logic. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8(4), 495–498.
Hájek, P. (2001). On very true. Fuzzy Sets and Systems, 124, 329–333.
Hájek, P. (2002). Some hedges for continuous t-norm logics. Neural Network World, 2(2), 159–164.
Lakoff, G. (1973). Hedges: A study in meaning criteria and the logic of fuzzy concepts. Journal of Philosophical Logic, 2, 458–508.
Laurence, S. & Margolis, E. (1999). Concepts and cognitive science. In: E., Margolis, & S., Laurence, (Eds.), Concepts: Core Readings (pp. 3–81). Massachusetts: The MIT Press.
Vanackere, G. (1997). Ambiguity-adaptive logic. Logique et Analyse, 159, 261–280
Vychodil, V. (2006). Truth-depressing hedges and BL-logic. Fuzzy Sets and Systems, 157(15), 2074–2090.
Wittgenstein, L. (1953). Philosophical investigations. New York: The MacMillan Company.
Zadeh, L. A. (1971). Quantitative fuzzy semantics. Information Sciences, 3, 159–167.
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van der Waart van Gulik, S. Adaptive Fuzzy Logics for Contextual Hedge Interpretation. J of Log Lang and Inf 18, 333–356 (2009). https://doi.org/10.1007/s10849-009-9084-y
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DOI: https://doi.org/10.1007/s10849-009-9084-y