An Analytic Tableau System for Natural Logic

In Maria Aloni, H. Bastiaanse, T. De Jager & Katrin Schulz (eds.), Logic, Language and Meaning. Springer. pp. 104-113 (2010)
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Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alternative approach would be to develop a general theory of the natural logic behind human reasoning and human information processing by studying formal logics that operate directly on linguistic representations. That this is possible we will try to make plausible in this paper. It will turn out that one level of representation, that of Logical Form, can meaningfully be identified with the language of an existing and well-understood logic, a restricted form of the theory of types. It is not difficult to devise inference systems for this language, and it is thus possible to study reasoning systems that are based directly on language
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Essays in Logical Semantics.van Benthem, J. F. A. K.
Meaning and Partiality.Muskens, Reinhard
Meaning and Partiality.Muskens, Reinhard

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