Partial Monotonic Protothetics |
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Authors: | Lepage François |
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Institution: | (1) Department of Philosophy, University of Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Qc, Canada, H3C 3J7 |
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Abstract: | This paper has four parts. In the first part, I present Le niewski's protothetics and the complete system provided for that logic by Henkin. The second part presents a generalized notion of partial functions in propositional type theory. In the third part, these partial functions are used to define partial interpretations for protothetics. Finally, I present in the fourth part a complete system for partial protothetics. Completeness is proved by Henkin's method 4] using saturated sets instead of maximally saturated sets. This technique provides a canonical representation of a partial semantic space and it is suggested that this space can be interpreted as an epistemic state of a non-omniscient agent. |
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Keywords: | protothetics propositional type theory partial logic partial functions monotonic logic saturated sets epistemic logic |
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