Prezados,
Seguindo com a tradição de manter sessões especiais de Lógica Matemática
nos encontros bilaterais entre a Sociedade Brasileira de Matemática e suas
homólogas de outros países nos últimos anos (Brasil-Espanha 2015,
Brasil-Italia 2016, Brasil-França 2019 e Brasil-Portugal 2022, não
esquecendo da palestra da Profa. Itala D'Ottaviano no Brasil-Estados Unidos
de 2008), sempre com o apoio da Sociedade Brasileira de Lógica,
Segue a programação da Sessão Especial de Lógica Matemática no 1st Joint
Meeting Brazil México in Mathematics, evento esse que vai ocorrer entre os
dias 08 e 12 de Setembro em Fortaleza, Ceará, no Hotel Mareiro.
A Sessão Especial de Lógica Matemática vai ocorrer nas tardes da segunda e
da terça-feira, dias 08 e 09 de Setembro.
Programação:
Lunes, 08 Septiembre
14h-14h30 Claudia Nalon (UnB)
14h30-15h Nancy Nunez (UNAM)
15h-15h30 Francisco Hernandez Quiroz (UNAM)
15h30-16h30 Coffee Break
16h30-17h Favio Miranda Perea (UNAM)
17h-17h30 Daniel Ventura (UFG)
17h30-18h Lourdes Gonzales Huesca (UNAM)
Martes, 09 Septiembre
14h-14h30 Ulises Ariet Ramos Garcia (UNAM Morelia)
14h30-15h Samuel Gomes da Silva / Ciro Russo (UFBA)
15h-15h30 Salvador Garcia-Ferreira (UNAM Morelia)
15h30-16h30 Coffee break
Resumos:
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Claudia Nalon (UnB (Brazil))
Title of the talk: Automated Reasoning for Non-Classical Logics
Abstract of the talk: We will discuss two different
resolution-based calculi for the multimodal logic Kn with particular focus
on the characteristics that have impact on theorem-proving. We will report
on experimental results and the influence of proof strategies and
processing techniques for both calculi.
Francisco Hern\'andez Quiroz (UNAM FCiencias (México))
Title of the talk: Inferential Information Complexity
Abstract of the talk: An analogous to Kolmogorov complexity can be
used to measure the epistemic contribution of deduction. Minimal proof
length (in terms of inferential steps) in decidable systems is a good
indication of the minimal information needed to prove a theorem. This
measure is independent of the chosen proof system, provided it meets some
natural requirements.
Salvador Garcia-Ferreira (UNAM (Morelia, México))
Title of the talk: Semigroup actions and filters
Abstract of the talk: We will show the importance of certain
filters on a semigroup when it acts on a compact metric space. Mainly, in
the study of the invariant closed subsets. We give several examples of such
filters in various semigroups. We present also examples of actions of
semigroups on countable compact metric spaces.
Samuel Gomes da Silva (UFBA (Brazil))
Title of the talk: On Forcing Axioms and Weakenings of the Axiom of
Choice\\
Abstract of the talk: We prove forcing axiom equivalents of two
families of weakenings of the Axiom of Choice (like the hundreds listed in
the standard reference Howard and Rubin, ``Consequences of the Axiom of
Choice''):
a trichotomy principle for cardinals isolated by L\'evy,
$H_\kappa$, and $DC_\kappa$, the principle of dependent choices generalized
to cardinals $\kappa$, for regular cardinals $\kappa$. Using these
equivalents we obtain new forcing axiom formulations of the Axiom of
Choice, $\mathbf{AC}$. A point of interest is that we use a new template
for forcing axioms. For the class of forcings to which we asks that the
axioms apply, we do not ask that they apply to all collections of dense
sets of a certain cardinality (as previously done by Viale and others), but
rather only for each particular forcing to a specific family of dense sets
of the cardinality in question.
Ciro Russo (UFBA (Brazil))
Title of the talk: Priestley-type Duality for positive MV-algebras \\
Abstract of the talk: In this talk we shall present a Priestley-type
duality between positive MV algebras and a suitable class of ordered fuzzy
topological spaces. The duality theorem will include, as special cases,
both the classical Priestley duality and the Stone-type duality proved by
the speaker in a previous work.
Ulises Ariet Ramos-Garcia (UNAM MatMorelia (México))
Title of the talk: Hindman-tall ideals and the Ramsey property for
pairs in ordered-union ultrafilters
Abstract of the talk: We will show an equivalence between the
Ramsey's property for pairs in ordered-union ultrafilters on FIN in terms
of Hindman-tall ideals on FIN. This characterization is useful to address
an old problem of A. Blass asking if every ordered-union ultrafilter has
the Ramsey's property for pairs. This work is in collaboration with Angel
Augusto Camacho-Acosta and Carlos L\'opez-Callejas.
Daniel Ventura (UFG (Brazil))
Title of the talk: Linearisation Based on Normalisation Strategies\\
Abstract of the talk: Linear terms/functions have interesting
properties, such as no infinite reductions, typability in polynomial time,
and simpler and optimised abstract machines for their execution, due to
their no-duplication operational semantics. Linearisation of
strong-normalising terms has been proposed based on typing information an
intersection types system provides. More recently, a weak-linearisation
procedure --originally defined through a static characterisation of virtual
redices, based on legal paths computed from the term syntactic tree--, was
devised based on a quantitative type system. In such a procedure, functions
not applied in any reduction path are not linearised. Therefore, the
quantitative system provides information related to a maximal normalisation
strategy. In this work, we explore linearisation procedures based on
different normalisation strategies.
Favio Ezequiel Miranda Perea (UNAM (México))
Title of the talk: TBA
Abstract of the talk: TBA
Lourdes del Carmen Gonzalez Huesca (UNAM (México))
Title of the talk: TBA
Abstract of the talk: TBA
Nancy Abigail Nunez Hernandez (UNAM-FES, Acatlan (México))
Title of the talk: Why AI is not going to take mathematicians' jobs
(or on the complexity of mathematicians' jobs)
Abstract of the talk: The rapid development of AI is causing a lot
of concern among many people working in a wide variety of fields: teachers,
journalists, lawyers, physicians, and even programmers are worried about
losing their jobs to some form of AI. The question that I want to explore
in this work is whether AI can also take mathematicians' jobs. In 1956,
G\"odel wrote to von Neuman inquiring whether "the reasoning of
mathematicians about yes-or-no questions can be completely replaced by
machines." (Hartmanis 1993, p. 6) This letter has become famous among
theoretical computer scientists interested in the open problem of
determining if P and NP are different complexity classes. Although G\"odel
was inquiring about an NP-complete problem (Buss 1995), a mathematician's
job is also directly related to coNP-complete problems; for instance, when
they have to decide whether a given sentence follows from some set of
axioms or other theorems. This work proposes that because of the complexity
of the problems mathematicians deal with, AI should not be able to take
their jobs so easily.
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Todos os interessados que possam comparecer, sintam-se fortemente
convidados !
Atenciosamente
[]s Samuel, em nome dos organizadores da Sessão (Samuel e João Marcos pelo
Brasil, Lourdes Huesca e Favio Miranda-Perea pelo México).
--
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