Natural Logic and Semantics
Two of the main motivations for logic and (model-theoretic) semantics overlap in the sense that both subjects are concerned with representing features of natural language meaning and inference. At the same time, the two subjects have other motivations and so are largely separate enterprises. This paper returns to the topic of language and logic, presenting to semanticists natural logic, the study of logics for reasoning with sentences close to their surface form. My goal is to show that the subject already has some results that natural language semanticists might find interesting. At the same time it leads to problems and perspectives that I hope will interest the community. One leading idea is that the target logics for translations should have a decidable validity problem, ruling out first-order logic. I also will present a fairly new result based on the transitivity of comparative adjective phrases that suggests that in addition to ‘meaning postulates’ in semantics, we will also need to posit ‘proof principles’.
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- 1.Ben-Avi, G., Francez, N.: Proof-theoretic Semantics for a Syllogistic Fragment. In: Dekker, P., Franke, M. (eds.) Fifteenth Amsterdam Colloquium. ILLC/Department of Philosophy, U. Amsterdam, pp. 9–15 (2005)Google Scholar
- 2.van Benthem, J.: Essays in Logical Semantics. Reidel, Dordrecht (1986)Google Scholar
- 3.van Benthem, J.: A Brief History of Natural Logic. In: Chakraborty, M., Löwe, B., Nath Mitra, M., Sarukkai, S. (eds.) Logic, Navya-Nyaya and Applications, Homage to Bimal Krishna Matilal. College Publications, London (2008)Google Scholar
- 4.Englebretsen, G.: Three Logicians. Van Gorcum, Assen (1981)Google Scholar
- 8.Łukasiewicz, J.: Aristotle’s Syllogistic, 2nd edn. Clarendon Press, Oxford (1957)Google Scholar
- 11.Moss, L.S.: Syllogistic Logics with Verbs. J Logic Computat 20, 761–793 (2010)Google Scholar
- 12.Moss, L.S.: Logics for Two Fragments Beyond the Syllogistic Boundary. In: Blass, A., Dershowitz, N., Reisig, W. (eds.) Studies in Honor of Yuri Gurevich. LNCS. Springer, Heidelberg (2010)Google Scholar
- 18.Pratt-Hartmann, I., Third, A.: More Fragments of Language. Notre Dame J. Formal Logic 47(2) (2006)Google Scholar
- 20.Saanchez Valencia, V.: Studies on Natural Logic and Categorial Grammar. Ph.D. thesis, Univ. of Amsterdam (1991)Google Scholar
- 21.Sommers, F.: The Logic of Natural Language. Clarendon Press, Oxford (1982)Google Scholar
- 22.Westerståhl, D.: Aristotelian Syllogisms and Generalized Quantifiers. Studia Logica XLVIII(4), 577–585 (1989)Google Scholar