Truth functionality and measure-based logics (1999)
| Venue: | Fuzzy Sets, Logics and Reasoning about Knowledge |
| Citations: | 5 - 4 self |
BibTeX
@INPROCEEDINGS{Boldrin99truthfunctionality,
author = {Luca Boldrin and Via Brennero and Claudio Sossai},
title = {Truth functionality and measure-based logics},
booktitle = {Fuzzy Sets, Logics and Reasoning about Knowledge},
year = {1999},
pages = {351--380},
publisher = {Kluwer Academic Publishers}
}
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Abstract
We present a truth-functional semantics for necessity-valued logics, based on the forcing technique. We interpret possibility distributions (which correspond to necessity measures) as informational states, and introduce a suitable language (basically, an extension of classical logic, similar to Pavelka’s language). Then we define the relation of “forcing ” between an informational state and a formula, meaning that the state contains enough information to support the validity of the formula. The subsequent step is the definition of a many-valued truth-functional semantics, by simply taking the truth value of a formula to be the set of all informational states that force the truth of the formula. A proof system in sequent calculus form is provided, and validity and completeness theorems are proved. 1
