Banca de QUALIFICAÇÃO: VITOR RODRIGUES GREATI

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
STUDENT : VITOR RODRIGUES GREATI
DATE: 11/10/2021
TIME: 09:00
LOCAL: Google Meet (link a divulgar)
TITLE:
KEY WORDS:

two-dimensional consequence relations, Hilbert-style proof systems, non-deterministic semantics, proof search

PAGES: 82
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUMMARY:

The present work proposes a two-dimensional Hilbert-style deductive formalism (H-formalism) for B-consequence relations, a class of two-dimensional logics that generalize the usual (Tarskian, one-dimensional) notions of logic. We argue that the two-dimensional environment is appropriate to the study of bilateralism in logic, by allowing the primitive judgements of assertion and denial (or, as we prefer, the cognitive attitudes of acceptance and rejection) to act on independent but interacting dimensions in determining what-follows-from-what. In this perspective, our proposed formalism constitutes an inferential apparatus for reasoning over bilateralist judgments. After a throughout description of the inner workings of the proposed proof formalism, which is inspired by the one-dimensional symmetrical Hilbert-style systems, we provide a proof-search algorithm for finite analytic systems that runs in at most exponential time, in general, and in polynomial time when only rules having at most one formula in the succedent are present in the concerned system. We delve then into the area of two-dimensional non-deterministic semantics via matrix structures containing two sets of distinguished truth-values, one qualifying some truth-values as accepted, and the other, some values as rejected, constituting a semantical path for bilateralism in the two-dimensional environment. We present an algorithm for producing analytic two-dimensional Hilbert-style systems for sufficiently expressive two-dimensional matrices, as well as some streamlining procedures that allow to considerably reduce the size and complexity of the resulting calculi. For finite matrices, we should point out that the procedure results in finite systems. In this document, we register the achieved results up to the present moment and indicate a plan for the developments to be included in the final version of this thesis.

BANKING MEMBERS:
Presidente - 1517271 - JOAO MARCOS DE ALMEIDA
Externo à Instituição - CARLOS CALEIRO - IST
Externo à Instituição - SÉRGIO ROSEIRO TELES MARCELINO - IT
Externo à Instituição - YONI ZOHAR - Bar-Ilan