I am trying again to list the talks that happened in the Seminar organized by Luiz Carlos Pereira at Phil-PUC. I'm just looking at my inbox, so there are probably some mistakes and confusions. I'd be grateful if people can correct me or send me better links to their webpages and papers.
The second semester of the Working Logician Seminar just finished (16 Dec 2020) with a great talk by
Elaine Pimentel. She talked about her work on
Title: Trying to understand resource consciousness
Elaine Pimentel DMAT/UFRN
Abstract:
We look at substructural calculi from a game semantic point of view,
guided by certain intuitions about resource conscious and, more
specifically, cost conscious reasoning. To this aim, we start with a
game, where player I defends a claim corresponding to a
(single-conclusion) sequent, while player II tries to refute that claim.
Branching rules for additive connectives are modeled by choices of II,
while branching for multiplicative connectives leads to splitting the
game into parallel subgames, all of which have to be won by player I to
succeed. The game comes into full swing by adding cost labels to
assumptions, and a corresponding budget. Different proofs of the same
end-sequent are interpreted as more or less expensive strategies for I
to defend the corresponding claim. This leads to a new kind of labelled
calculus, which can be seen as a fragment of SELL (subexponential linear
logic). Finally, we generalize the concept of
costs in proofs by using a semiring structure, illustrate our
interpretation by examples and investigate some proof-theoretical
properties.
The talk assumes *no prior knowledge* on games or substructural logic. Only a basic notion of sequent systems is advisable. This is a joint work with Timo Lang, Carlos Olarte and Christian G. Fermüller.
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Before that, on the 9th Dec we had Prof Mattia Petrolo's talk
TITLE: A Constructivist Reading of the Epsilon Calculus
SPEAKERS. Mattia Petrolo (UFABC), Elio La Rosa (LMU Munich)ABSTRACT. The aim of this work is to provide a constructivist reading of Hilbert's epsilon calculus. This goal is achieved in two steps, one philosophical and the other logical. First, we investigate
in which sense the epsilon calculus can be seen, from a broadly Kreiselian perspective, as a way
of providing a constructive analysis of classical logic and mathematics. In order to highlight the
constructive aspects of this calculus, our strategy is to implement it in the general proof theoretic setting provided by (a variant of) Gentzen's sequent calculus.
In particular, a cut-elimination algorithm for a version of the epsilon calculus is provided.
Thus, in the second part of this work, we show how a given notion of constructivity can bedisplayed via the epsilon calculus.
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Title: The pragmatic structure of mathematics
We explore many linguistic facets that permeate mathematical
proofs. To do so, we analyze mathematics through the lens of speech act
theory, focusing on those illocutionary aspects which are peculiar to
the mathematical discourse. Our analysis includes both the single speech
acts that occur in proofs and the delicate interplay of such acts.
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And on 1 de dezembro às 11h00, horário de Brasília (15h00 CET) there was a talk by
Prof Peter Verdee:
Title: A universal graph-theoretic criterion for relevance
Abstract
In this talk I present work in progress by my FNRS MIS funded research team (Pilar Terres, Pierre Saint-Germier, Joao Daniel Dantas) working on explanatory inference. We came up with a criterion for relevance of the entailment relation, relative to a given logic.
One of the weak criteria of relevance presented in the literature is
the principle of variable sharing: if a (multiple conclusion) sequent is
relevantly valid then every formula in the sequent needs to have at
least one variable in common with the other formulas in the sequent. I
present a couple of cases from which it should be clear that this
criterion (while being necessary) certainly is not sufficient for
relevance. We solve these problems by analyzing relevance in terms of
connectivity. The idea is to say that a sequent is relevantly valid iff
a connected graph (of a specific nature) can be established that
contains all of the formulas of the sequent. The basis of this idea is
the concept of a constitution of a logic. This is a set of sequents that express full logical grounds of all formulas of the language of the logic (the grounded formula of each sequent is underlined, the non-underlined formulas are the partial grounds--examples are "A,B>A&B", "A&B>A" and "A, A->B > B" in the case of classical logic).
The partial grounds (the non-underlined formulas) of each formula
determine the way in which formulas of the potentially relevant sequents
can be connected to other formulas of the sequent. We will present and
motivate the criterion, give a couple of examples, and present some
graph-theoretical results concerning this criterion.
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Title: A maximalist view on the meaning of logical connectives
Abstract: The aim of this talk is to explore the consequences that
minimalism for logical connectives (the view that the meaning is
determined by their left and right rules in different sequent calculus
languages), together with logical pluralism, has in our undertanding of
logical connectives in natural language. I want to suggest an
alternative view: the meaning of logical connectives is determined by
their left and right rules in the full-structural classical logic,
and hence, the meaning of the logical vocabulary is not necessarily
determined by their inferential role in the different logics that a
pluralist endorses.
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Title: The BA plan: how to recapture classicality in the ST-hierarchy
Abstract. Anti-exceptionalism about logic
is the approach that logical theories have no special epistemological
status. Such theories are continuous with scientific theories.
Contemporary anti-exceptionalists include data about semantic paradoxes
as a part of the logical evidence. Exploring the Buenos Aires plan, the
recent development of the metainferential hierarchy of ST-logics shows that there are multiple options to deal with such paradoxes. There is a whole ST-based hierarchy, of which LP and ST itself are only the first steps. The logics in this hierarchy and STω are
also options to deal with semantic paradoxes. This talk explores these
responses analyzing some reasons to go beyond the first steps. I
show that LP, ST and the logics of the ST-hierarchy
offer different diagnoses for the same evidence: the inferences and
metainferences the agents endorse in the presence of the
truth-predicate. But even if the data is not enough to adopt one of
these logics, there are other elements to evaluate the revision of
classical logic. How close should we be to classical logic? Which logic should be used during the revision? Should a logic be closed under its own rules? How could a logic
obey the validities they contain? And mainly, Which is the best
explanation of the logical principles to deal with semantic paradoxes? I
will argue that, if the answers to these questions are provided by an
antiexceptionalist perspective, ST-metainferential logics in general—and STTω in particular—are the best available options.
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Professor Abílio Rodrigues (18/11/2020)
Title: Reflective Equilibrium and Logical Pluralism
The aim of this talk is to propose a pluralist view of logic that
makes possible a peaceful coexistence between classical logic and some
paraconsistent and paracomplete logics. The central point is to
understand the inference rules of classical, intuitionistic, Nelson's
N3, Belnap-Dunn 4-valued logic, and BLE (the basic logic of evidence)
as a result of two ingredients: i. inferential practices based, in
each case, on a fundamental semantic notion; ii. reflective
equilibrium. The result of combining logical pluralism with reflective
equilibrium is a weak form of revisionism, according to which logic is
not really revised. The idea is rather that different formal systems
are concerned with different properties of propositions, and therefore
are appropriate to different contexts of reasoning. (Joint work with
Marcos Silva)
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We started this second half of the Seminar with four presentations by Prof Hermann Haeusler,
Título: Redundancy in huge Natural Deduction proofs or how to obtain polynomial certificates for Non-Hamiltonian graphs
by Edward Hermann Haeusler and Lew Gordeev
In this talk, we take the family of normal proofs of the tautologies of the purely implicational minimal logic
as a family of super-polynomially bounded or huge sized objects. We
use the notion of (atomic) expanded and mapped normal (EmND) proofs to
prove that almost every huge EmND proof that has a linearly bounded
height is highly redundant. We show that for almost all proofs of such
family there is at least one sub-proof or derivation that is repeated
super-polynomially many times.
This result points out to a refinement of
compression methods previously presented and an alternative and simpler
proof that CoNP=NP.
(photo by Daniel Schwabe)
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