**Topic:**

**GENERAL LOGIC**

## Logic Inference in Polynomial Format

By Walter Carnielli

The methods described in this paper have a promising potential to any truth-functional multi-valued logic: there is an exciting area of research in designing new proof theory techniques for such logics, and simplifying applications to multi-valued logics in decision tables and discovering patterns, as in several other fields (it is well-known that multi-valued logics find applications in artificial intelligence, database theory and data mining, modeling reasoning and model checking, for instance). It is important to emphasize that the method is also plainly applicable to non-finite valued logics, and also to represent binary semantics for many-valued logics5 (cf. [13]) and even to quantum circuits and quantum gates (cf. [1]). The arguments advanced here try to conceptualize this approach, in particular when extended to quantification and non-finite valued logics, as inheritance of an admirable legacy in the mathematical thinking, which may have been disregarded by logicians.

Source: CLE e-prints