Abstract
This chapter has three discussions related to one of Johan van Benthem’s longstanding interests, the areas of interaction of logic and linguistics. We review much of what is known on the landscape of syllogistic logics. These are logics which correspond to fragments of language. The idea in this area is to have complete and decidable systems. Next we present a very simple form of dynamic logic, essentially a logic of two worlds with a back-and-forth arrow between them. This is then related to an issue in dynamic semantics, the logic of “and then”. Our last discussion is related to an area which van Benthem again did so much to stimulate, the area of monotonicity reasoning in language. We connect the topic to reasoning in elementary mathematics. We formalize a monotonicity calculus following van Benthem and Sánchez Valencia, and we interpret this on hierarchies of preorders rather than sets.
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Notes
- 1.
This material is adapted from [7].
References
van Benthem J (1986) Essays in Logical Semantics. In: Studies in linguistics and philosophy, vol 29. D. Reidel Publishing Co., Dordrecht.
van Benthem J (1991), Language in Action. In: Studies in logic and the foundations of mathematics, vol 130. North-Holland, Amsterdam.
van Benthem J (2008) A brief history of natural logic. In: Mitra MN, Chakraborty M, Löwe B, Sarukkai S (eds) Logic, Navya-Nyaya and applications, homage to Bimal Krishna Matilal. College Publications, London
Bernardi R (2002) Reasoning with polarity in categorial type logic. PhD thesis, University of Utrecht.
Icard III TF, Moss LS (2014) Recent progress on monotonicity, Linguistic Issues in Language Technology 9(7).
MacCartney B, Manning CD (2009) An extended model of natural logic. In: Proceedings of the eighth international conference on computational semantics (IWCS-8), Tilburg, Netherlands.
Moss LS (2013) Invitation to possible worlds. Indiana University, Bloomington (Unpublished text for a modal logic course)
Nairn R, Condoravdi C, Karttunen L (2006) Computing relative polarity for textual inference. Proceedings of ICoS-5 (inference in computational semantics). Buxton, UK, pp 20–21
Pratt-Hartmann I, Moss LS (2009) Logics for the relational syllogistic. Review of Symbolic Logic 2(4):647–683
Sánchez-Valencia VM (1991) Studies on natural logic and categorical grammar. PhD thesis, University of Amsterdam.
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Moss, L.S. (2014). Three Etudes on Logical Dynamics and the Program of Natural Logic. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_26
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DOI: https://doi.org/10.1007/978-3-319-06025-5_26
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