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]

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:

Next scheduled  talks via “Conferência Web”:

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

14/04/21, 16:00 – Itala M. Loffredo D’Ottaviano & Evandro Luís Gomes

Baptizing Paraconsistent Logic: the unique touch of Miró Quesada

Centro de Lógica, Epistemologia e História da Ciência

Universidade de Campinas


In this paper we present and analyse the principal historical events surrounding the creation of the word ‘paraconsistent’, as well as its introduction as the name for inconsistent but non-trivial formal systems. Initially, these systems were called the ‘theory of inconsistent formal systems’ by Newton da Costa when he introduced his C-systems in 1963. In the early 1970’s, however, da Costa asked Francisco Miró Quesada to look for suggestions for a meaningful name for this new family of formal systems. The goal was achieved in correspondence exchanged in 1975, when Miró Quesada suggested to Newton da Costa an all-embracing name which finally came to predominate. Quesada master’s touch into history of paraconsistent logic was presented to the international academic community in a conference delivered by him at the Third Latin American Symposium on Mathematical Logic (III SLALM), held in 1976 at the University of Campinas.

07/04/2021, 16:00 – Guilherme Vicentin de Toledo

RNmatrizes e a hierarquia de da Costa

Centro de Lógica, Epistemologia e História da Ciência

Universidade de Campinas


RNmatrizes e a hierarquia de da Costa (Abstract)_Página_1 RNmatrizes e a hierarquia de da Costa (Abstract)_Página_2 RNmatrizes e a hierarquia de da Costa (Abstract)_Página_3

31/03/2021, 16:00 – Rodolfo C. Ertola-Biraben

The Emergence of Lattice Theory

Centro de Lógica, Epistemologia e História da Ciência

Universidade de Campinas


Our talk traces the origin of Lattice Theory in the nineteenth century. It will be organized
around the notions of modularity and distributivity. In particular, it will include comments on passages from the writings of Peirce [2], Schr ̈oder [3], and Dedekind [1].

[1] Dedekind, Richard. Ueber die von drei Moduln erzeugte Dualgruppe. Mathematische Annalen
53, 1900.
[2] Peirce, Charles. On the algebra of logic. American Journal of Mathematics 3(1), 1880.
[3] Schr ̈oder, Ernst. Vorlesungen ̈uber die Algebra der Logik. Erster Band, Leipzig, Teubner, 1890.

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.


[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.


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.