Por Bruno Dinis (Universidade de Évora and CIMA - Centro de Investigação em Matemática e Aplicações).
Abstract: In this talk I will present a formal logic called Natural Term Logic (NTL) which is based on the syntactic and logical structure of natural language. NTL can be seen as a refinement of the ideas of Quine's paper 'Variables Explained Away' and the technical concepts introduced by Bealer and Zalta. NTL is more fine-grained than Bealer's first-order intensional logic (BL): there is a many-to-one correspondence $\nu$ between NTL terms, closed BL terms and a one-to-one correspondence $\beta$ which assings to each BL term a corresponding NTL term. I will define a series of reductions on NTL for which every NTL term T reduces to a unique normal term N. It is possible to show that $\nu$ is invariant under these reductions and that $\beta \nu T = N$, thus closed terms of BL represent normal NTL terms. The above results depend on a mathematical treatment of permutations and equivalence relations on finite totally ordered sets, a theory we call plectology and which we believe to be of interest in its own right.
(Joint work with Clarence Protin)
