Larry Moss (Indiana University)
Natural Logic
Abstract: A central motivation for modern logic is that it provides a tool to represent natural language meaning and inference. One of the motivations of first-order logic is precisely that one can translate significant aspects of language into it, and in addition one can use it in connection with the foundations of mathematics. This talk returns to the topic of language and logic, and proposes new logical systems for the area. One leading idea is to propose logics with a decidable validity problem, ruling out full first-order logic. Indeed, we are interested in finding decidable fragments of language, just as others have asked for decidable fragments of first-order logic. We also axiomatize the logics, just to see what they look like. The overall topic of this research could be interesting to those pursuing natural language semantics and also to people in computational linguistics who work on inference. It also could be of interest to historians of logic, since in effect, we are asking what traditional logic would have evolved into if it had the mathematical tools that are so prominent in modern logic. The talk mentions a number of technical results, and they are closest to algebraic logic, model theory and descriptive complexity theory. |
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