Colloquium Logicae Web Conference – CLE/Unicamp

Link permanente para participar dos seminários /

The link to the seminars will be available only by email.

Contact: edson.vinber92[at]gmail.com

Colloquium Logicae at CLE is now partner of the “Logic Supergroup”

The logic seminars connected to the course HF912 have been cancelled due to the interruption of activities at Unicamp in face of the Coronavirus from March 13th, with the final date to be evaluated.

Aa all scheduled in-person meetings have been  cancelled, we are inaugurating a virtual session of the  Colloquium Logicae, traditional conferences held the Centre for Logic, Epistemology and the History of Science at Unicamp, now linked to the “Logic Supergroup”. The website is:
https://logic.uconn.edu/supergroup/


Next scheduled  talks via “Conferência Web”:
https://conferenciaweb.rnp.br/spaces/unicamp-cle-colloquium-logicae

Please enter as  “anonymous” unless you have an RNP account

30/09/2020, 16:00h – Rafael Testa

Representação do Conhecimento e Raciocínio: aplicações e motivações às lógicas paraconsistentes

Centro de Lógica, Epistemologia e História da Ciência

Universidade de Campinas

Abstract. A Representação do Conhecimento e Raciocínio desempenha um papel central na Inteligência Artificial, sendo uma de suas áreas mais antigas. Seu estudo cobre uma ampla gama de tópicos, incluindo a modelagem de raciocínio em domínios específicos (como em diagnósticos médicos e no direito), o desenvolvimento de softwares para prova automatizada de teoremas, o desenvolvimento de banco de dados, bem como estudo do raciocínio humano. Neste seminário veremos alguns exemplos de aplicação de lógicas paraconsistentes, notadamente as lógicas da inconsistência formal, nesta área de estudo. Novas perspectivas e possíveis trabalhos futuros serão apresentados.

14/10/2020 (16:00h) – Guilherme Grudtner

A Medida do Círculo: Uma tradução do texto ΚΥΚΛΟΥ ΜΕΤΡΗΣΙΣ de Arquimedes

Instituto de Filosofia e Ciências Humanas

Universidade de Campinas

Abstract. Arquimedes de Siracusa foi um matemático, físico, astrônomo e engenheiro grego que viveu no século III a.C. (c. 287 a.C. – c. 212 a.C.). Sobre sua biografia, restam-nos pouquíssimos dados, dentre os quais, alguns fatos pitorescos. Porém, seus trabalhos tiveram enorme influência no desenvolvimento da matemática e da física.

Apresentamos, aqui, uma tradução do texto de Arquimedes intitulado ΚΥΚΛΟΥ ΜΕΤΡΗΣΙΣ (Kyklou Metresis) – A Medida do Círculo. A tradução foi efetuada segundo uma perspectiva quase literal. Desse modo, tentamos preservar ao máximo a estrutura original do texto grego, incluindo entre colchetes palavras que podem auxiliar a compreensão do leitor. Tal abordagem pode ocasionar uma sensação de estranheza similar à de quem lê o original, de acordo com o estilo do próprio Arquimedes. Nesse texto, o matemático grego estabelece um modo de se obter a área do círculo, bem como, uma aproximação da razão entre o comprimento do círculo e seu diâmetro, o que nos permite determinar um valor aproximado para constante π.

21/10/2020 (16:00h) – Pedro Carrasqueira

Parts of (inter)actions: Game-based truthmaker semantics for deontic logic

Instituto de Filosofia e Ciências Humanas

Universidade de Campinas

Abstract. Standard deontic logic (SDL) is riddled with puzzles that point out to its limited, even inadequate expressive power as a deontic logic. Many alternatives to SDL have been proposed which purport to deal with (at least some of) them. It seems to me, however, that the proposals that are to be found in extant literature have met the challenges presented by the puzzles of SDL with partial success at best, as some of the puzzles can be reiterated in some of those logics, and arguably none of the available alternatives to SDL tackle all or even most of them in an uniform, principled fashion. Recently, however, Kit Fine introduced a deontic logic, based on so-called truthmaker semantics, that seems to me to be on the right track. Albeit interesting in its own right as a (supposedly) action-based deontic logic, his semantics lacks the capability to model aspects of interaction that I believe are essential to make sense of normative discourse.

In this talk, I present for a language of deontic logic a (simplified version of a) truthmaker semantics alternative to the one proposed by Fine, and then discuss how it fares in dealing with SDL’s puzzles. It is based on extensive games with some additional features. It models norms as choices on terminal positions of games, and it takes positions as truthmakers, making use of the structural properties of extensive games in order to provide what I believe are intuitively plausible interpretations for both the propositional and the deontic operators of the language.

28/10/2020 (16:00h) – Edward Zalta* and Uri Nodelman**

Number Theory Without Mathematics

Stanford University (Senior Research Scholar, Stanford University)*
Stanford University (Senior Research Engineer, Stanford University)**

Abstract. No specifically mathematical primitives or axioms are required to derive second order Peano Arithmetic (PA2) or to prove the existence of an infinite cardinal. We establish this by improving and extending the results of Zalta 1999 (“Natural Numbers and Natural Cardinals as Abstract Objects”, J. Philosophical Logic, 28(6): 619-660), in which the Dedekind- Peano axioms for number theory were derived in an extension of object theory. We improve the results by developing a Fregean approach to numbers that accomodates a modal setting, yielding numbers that are stable across possible worlds, even though the equivalence classes of equinumerous properties vary. To extend the results, we (a) prove a Recursion theorem (which shows that recursive functions are relations grounded in second-order comprehension), (b) derive PA2, and (c) re-derive the existence of an infinite cardinal and (d) derive the existence of an infinite set (where sets are defined as non-mathematical extensions of properties). Since the background framework of object theory has no mathematical primitives and no mathematical axioms, we have a mathematics-free foundation for number theory.

04/11/2020 (16:00h) – Bruno Mendonça

Game-theoretic semantics, quantifiers and logical omniscience

Instituto de Filosofia e Ciências Humanas/CAPES

University of Campinas

Abstract. Logical omniscience, a key theorem of normal epistemic logics, states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general consider logical omniscience unrealistic, there is no clear consensus on how it should be restrained. The challenge is most of all conceptual: we must find adequate criteria for separating obvious logical consequences (i.e., consequences for which epistemic closure certainly holds) from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, based on urn semantics [5], an expressive fragment of classical game semantics that weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of a given first order argument or sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is required to obtain a more accurate solution of the problem. In this paper, I propose one such improvement based on two claims. First, to avoid the difficulties faced by accounts of logical obviousness in terms of easy provability [e.g., 2, 3, 4], I argue that we should rather conceive logical knowledge in terms of a default and challenge model of justification [1, 6]. Secondly, I sustain that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be roughly formulated as follows: (R ∀) when inquiring on the truth-value of a sentence of the form ∀x p, an individual might be unaware of all substitutional instances that this sentence accepts, but at least she must know that, if an element a is given, then ∀x p holds only if p(a/x) is true. Both claims accept game-theoretic formalization in terms of a refinement of urn semantics. I maintain that the system so obtained (US+R ∀) affords an improved solution of the logical omniscience problem. To do this, I prove that it is complete for a special class of urn models and, subsequently, I characterize first order theoremhood in this logic. Based on this characterization, we will be able to see that the classical first order validities which are not preserved in US + R ∀ form a class of formulae such that we have semantic reasons to affirm that an individual can present perfect linguistic competence and still ignore their logical truth.

References

[1] Brandom,R. Making it Explicit: Reasoning, Representing, and Discursive Commitment, Cambridge: Harvard University press, 1998.

[2] D’Agostino, M.”Tractable depth-bounded logics and the problem of logical omniscience”, pages 245–275,in H.Hosni and F. Montagna (eds.), Probability, Uncertainty and Rationality, Dordrecht: Springer, 2010.

[3] Jago, M. “Logical information and epistemic space”, Synthese, 167, 2 (2009): 327–341.

[4] Jago, M.”The content of deduction”, Journal of Philosophical Logic, 42,2(2009):317–334.

[5] Rantala,V. “Urn models: a new kind of non-standard model for first-order logic”, pages 347–366, in E. Saarinen (ed.) Game-Theoretical Semantics, Dordrecht: Springer, 1979

[6] Williams, M., Problems of Knowledge, Oxford: Oxford University Press, 2001.

11/11/2020 (16:00h) – Gesiel Borges da Silva

Logic and the problem of evil: an axiomaticapproach to theodicy via modal applied systems

Instituto de Filosofia e Ciências Humanas

Universidade de Campinas

Abstract. Edward Nieznanski developed in 2007 and 2008 two formal systems in order to deal with a variety of the problem of evil associated with aformulation of religious determinism. We revisited his two systems to give amore suitable form to them, reformulating them in first-order modal logic. Thenew resulting systems, called N1 (Da Silva & Bertato, 2019) and N2, havemuch of the original basic structure, and many axioms, definitions, and theo-rems still remain, but some different results are obtained. Both N1 and N2 aim at solving the logical problem of evil through the refutation of a version ofreligious determinism, showing that the attributes of God in Classical Theism, namely, those of omniscience, omnipotence, infallibility, and omnibenevolence, when adequately formalized, are consistent with the existence of evil in theworld.Furthermore, our research found that an underlying minimal set of axioms isenough to settle the questions proposed. Thus, we developed a minimal system, called N3, that solves the same issues tackled by N1 and N2, but with lessassumptions than the previous systems. This presentation aims at exposingthese three systems, developed during my Master’s research. The research is part of the project “Formal Approaches to Philosophy of Religion and Analytic Theology”, leaded by Prof. Fábio Bertato and Profa Itala D’Ottaviano, and granted by the John Templeton Foundation.

References

Da Silva, G. B., & Bertato, F. M. (2019). A first-order modal theodicy: God, evil, and religious determinism. South American Journal of Logic, 5(1), 49-80.

18/11/2020 (16:00h) – Juliana Bueno Soler

Pluralismo Probabilístico

Faculdade de Tecnologia/Instituto de Filosofia e Ciências Humanas

Universidade de Campinas

Resumo. Desde as ideias seminais de Leibniz, Boole, Pascal e Fermat entre outros, as teorias da probabilidade se dividem em duas variedades distintas: (i) as teorias estocásticas à lá Kolmogorov, preferidas por físicos, matemáticos e engenheiros; (ii) as teorias epistêmicas, preferidas por filósofos, lógicos e cientistas da computação.

Embora as duas vertentes convivam harmoniosamente no âmbito da lógica clássica, esta postura é desafiada quando se leva em conta o pluralismo lógico contemporâneo. Pretendo defender que um pluralismo probabilístico é perfeitamente aceitável, levando em conta a conexão entre lógica e probabilidade, ilustrando com exemplos e estudo de casos a defesa racional deste enfoque.

25/11/2020 (16:00h) – Guilherme Toledo

Lógicas de Incompatibilidade associadas a LFI’s:
definição, semânticas, não-caracterizabilidade e história

Instituto de Filosofia e Ciências Humanas

Universidade de Campinas

Abstract. Enquanto pesquisávamos certas semânticas de caráter não-determinístico para lógicas de inconsistência formal (LFI′s), notamos que a inclusão de um conectivo binário, capaz de codificara consistência de uma fórmula, à mbC [1] era capaz de simplificar notavelmente estruturas de Fidel [2] generalizadas para este sistema. Uma interpretação natural para o conectivo com as propriedades suficientes para tal simplificação seria a de incompatibilidade entre fórmulas.

Este acidente de pesquisa nos levou a derivar uma sintaxe básica para as lógicas que, por uma razão ou outra, substituíssem o conceito de consistência pelo de incompatibilidade, que mostrou-se ser surpreendentemente simples e, ao mesmo tempo, expressiva. Essencialmente, não exigimos mais da incompatibilidade do quê comutatividade e uma forma adequada de ex contradiction quodlibet, não envolvendo negação mas sim incompatibilidade. E, contra nossas expectativas,as lógicas de incompatibilidade, como passamos a chamá-las, se mostraram capazes de reobter, através de traduções conservativas [3], muitas das lógicas de inconsistência formal.

Os sistemas assim obtidos se mostraram adequados para semânticas de bivalorações bastante intuitivas e tratamento através de estruturas de Fidel; mas, talvez mais importante, muitos dos métodos mais usuais para tratamento de sistemas lógicos falham no caso específico das nossas lógicas, já que, como mostraremos, elas não admitem algebrização de acordo com Blok e Pigozzi [4]. Também indicaremos estudos no sentido de não-caracterizabilidade destes sistemas por matrizes não-determinísticas finitas, nos quais seguimos os argumentos de Avron em [5].

Finalmente, estabelecemos um contato destas lógicas com o resto da literatura. Além de altamente intuitivas, capazes de recapturar consistência e ótimos exemplos de sistemas de difícil tratamento que podem ser caracterizados pelas novas semânticas não-determinísticas que, precisamente, motivaram todo este desenvolvimento aqui relatado, nossas lógicas de incompatibilidade partilham muito das lógicas de incompatibilidade desenvolvidas por Brandom [6] e Peregrin [7]. Ambos os autores fazem parte de um programa que tenta reformular sistemas lógicos, usualmente de caráter dedutivo, em termos de incompatibilidade; e embora as semelhanças sejam muitas, nossos sistemas carregam características próprias explicadas somente pelo ambiente paraconsistente em que foram pensados.

Referências.

[1] Carnielli, Walter; Coniglio, Marcelo Esteban. 2016. Paraconsistent Logic: Consistency, Contradiction and Negation. Springer.
[2] Fidel, Manuel M.. 2003. Nuevos enfoques en Lógica Algebraica. Ph.D. thesis.
[3] da Silva, Jairo J., Itala M. L. D’Ottaviano, and Antonio M.A. Sette. 1999. Translations between logics. In Models, algebras and proofs. New York: Marcel Dekker.
[4] Blok, Don; Pigozzi, W. J.. 1989. Algebraizable Logics. Memoirs of the American Mathematical Society.
[5] Avron, Arnon. 2006. Non-deterministic semantics for logics with a consistency operator. International Journal of Approximate Reasoning.
[6] Brandom, Robert B.. 2008. Between Saying and Doing: Towards an Analytic Pragmatism. Oxford University Press.
[7] Peregrin, Jaroslav. 2011. Logic as based in incompatibility. The Logica Yearbook 2010, College Publications.

02/12/2020 (16:00h) – David Fuenmayor

Generalized topological semantics for weak negations and applications to the analysis of Gödel’s incompleteness theorem

Department of Mathematics and Computer Science

Freie Universität Berlin

Abstract. This talk is divided into two parts. First, I introduce a sort of generalized topological semantics for paraconsistent and paracomplete (e.g. intuitionistic) logics by drawing upon early works on topological Boolean algebras (cf. Kuratowski, Zarycki, McKinsey & Tarski). In the second part, I present some preliminary joint work with Walter Carnielli [1] which formalizes the ‘last mile’ of the proof of Gödel’s incompleteness theorem using some weak paraconsistent Logics of Formal Inconsistency (a special case of the logics discussed in the first part). All presented results have been obtained with help of the proof assistant Isabelle/HOL. The idea is to motivate a (hopefully lively) discussion on the use of automated reasoning with non-classical logics in the formalization and (re)interpretation of influential meta-mathematical results.

[1] W. Carnielli, D. Fuenmayor (2020). Gödel blooming: the incompleteness theorems from a paraconsistent perspective. Preprint. Vol. 19 No. 4 (2020) CLE e-prints (https://www.cle.unicamp.br/eprints/index.php/CLE_e-Prints/issue/view/243)

09/12/2020 (16:00h) – Edson Bezerra

Formal systems and their informal notions: the case of (some) paraconsistent logics

Instituto de Filosofia e Ciências Humanas

Universidade de Campinas

Abstract. Kreisel’s squeezing argument (1967) shows that there is an informal notion of validity which is irreducible to both model-theoretic and proof-theoretic validity of First-Order Logic (FOL), but coextensive with both formal notions. His definition of informal validity as truth in all structures received some criticisms in the literature for being heavily model-theoretical (Smith (2011) and Halbach (2020)). However, because of its simple and schematic form, variants squeezing argument has been presented for capturing other intuitive notions of validity closer to our pre-theoretical notion of validity (Shapiro, 2005). Therefore, the different squeezing arguments we find in the literature show that there are other informal notions of logical validity, which are coextensive with their corresponding formal definition of logical validity. In this talk, we argue for an even form of pluralism, showing that squeezing arguments cannot squeeze in the uniqueness of the corresponding informal notion. Indeed, we maintain that a complete logical system can be compatible with different notions of informal validity. Second, we will wonder whether such underdeterminedness occurs on non-classical logics. In this talk, we will concentrate our analysis to the case of the Logics of Formal Inconsistency.