Centro de lógica, epistemologia e história da ciência

RatioLog

Rationality, Logic and Probability

FAPESP Grant 2020/16353-3

Project Description

Logic, probability theory, and theories of rationality are intricately linked. While the first two serve as fundamental tools in the formal examination of reasoning, the latter is valued for its ability to elucidate, guide, and assess actions. This thematic project aims to explore the relationship between logic and its various generalizations, including many-valued, fuzzy, intuitionistic, paraconsistent, and modal logics. Additionally, the concept of probability and its diverse generalizations, such as credal calculi, belief functions, plausibility measures, and new axiomatics for probability and other measures, will be investigated.

The exploration of common generalizations for both logic and probability is also contemplated, with applications spanning philosophy, linguistics, artificial intelligence, and the philosophy of science and mathematics, emphasizing the interconnections among these domains. Throughout the development of this project, other areas and topics closely associated with rationality that intersect with the primary formal lines may be also investigated. These include social choice theory, rational decision making, game theory, Bayesian epistemology, and artificial intelligence, among others.

Activities

Task I

Evidence, Probability and Logic








- Subtask I.1: Probability as depending on Logic: Foundations and Applications

– Subtask I.2: Generalizations of Probability Measures: General Credal Calculi

– Subtask I.3: Certain and Uncertain Reasoning: Belief Revision and Rational Principles of

Intelligibility

Task ii

Non-Deterministic Methods: ​Hyperalgebraic Structures, ​Modalities, and

Extensions of Probabilities








– Subtask II.1: Hyperalgebraic ​Structures, Non-Determinsitc semantics ​and probabilities

– Subtask II.2: Total uncertainty: ​Paraconsisteny, Fuzziness, Uncertain ​Probabilities

– Subtask II.3: Probability Measures and ​Modalities

task iii

Contradictions, Evidence and Truth: Towards a Global Philosophy of

Paraconsistency










– Subtask III.1: Foundations of probability

– Subtask III.2: Axiomatic principles for absolute and relative (conditional) probability

– Subtask III.3: Probability and rational argumentation

Principal Investigators

MARCELO CONIGLIO

(IFCH/CLE - UNICAMP)


wALTER CARNIELLI

(IFCH/CLE - UNICAMP)


juliana BUeno-soler

(cle/ft - UNICAMP)


Associate Researchers

rodolfo ertola biren

researcher at cle - unicamp

Mariana Matulovic

UNESP - Tupã, SP

fábio maia bertato

researcher at cle - unicamp

Carlile Lavor

MAT- IMECC- UNICAMP

JULIO M. STERN

MAT - IME - USP

PhD Students and

Post-Doctoral Researchers

PhD Students

  • Rafael Ongaratto (CLE/ IFCH-UNICAMP)
  • Gabriel Rocha (CLE/ IFCH-UNICAMP)
  • Renato Reis Leme (CLE/ IFCH-UNICAMP)
  • Daniel Diniz (CLE/ IFCH-UNICAMP)
  • Mahan Vaz Silva (CLE/ IFCH-UNICAMP and Ruhr-Universität
  • Bochum - RUB)
  • Maira Bitencourt (CLE/ IFCH-UNICAMP)
  • Alan René Mantezana (CLE/ IFCH-UNICAMP)

Post-Doctoral Researchers

  • Pedro Henrique Carrasqueira (CLE/IFCH ​- UNICAMP)
  • Guilherme Toledo (Bar-Illan University, ​Israel)

Other Researchers and External Participants

  • Newton Marques Peron (UFFS - Chapecó, SC)
  • Abílio Rodrigues (CLE and UFMG - Belo Horizonte, MG)
  • Henrique Antunes (UFBA, Salvador, BA)
  • Juan Carlos Agudelo (EAFIT-Medellin, Colômbia)
  • Francesc Esteva (Artificial Intelligence Research Institute, Universitat Autonoma de Barcelona, Spain)
  • Tommaso Flaminio (Artificial Intelligence Research Institute, Universitat Autonoma de Barcelona, Spain)
  • LluisGodo (Artificial Intelligence Research Institute, Universitat Autonoma de Barcelona, Spain)

Predecessors

This project is a sequel of two predecessors, namely:


ConsRel. From March 2004 to April 2010, this project has focused on scrutinizing the notion of consequence relation, emphasizing specific methods for combining logics and investigating the semantical, algebraic and computational aspects of the resulting combined systems, including aspects of efficient consequence relations.


LogCons. From 2010 to 201, this project has focused on questions of combining semantics and non-classical logics, including aspects of new models of computation, such as quantum computation and information, quantum algorithms and quantum cryptography. Several papers and some books have been published within the topics of combinations of logics, foundations of paraconsistent logics, theorem proving, AI, belief revision, foundations of probability, among others. Both projects were really successful, and fomented the integration among experienced researchers from Unicamp, USP and UNESP. Alongside efficient dissemination of results in papers and national and international conferences, the relevant results can also be found in ten scientific reports made public at:


http://www.cle.unicamp.br/teste123/grupoglta/Thematic-Consrel-FAPESP and

http://www.cle.unicamp.br/teste123/grupoglta/Thematic-LogCons-FAPESP

Innovation and Intellectual Production

The project will count with some Master grants, PhD grants and Post-Doc grants. Presently we already have 2 post-doc positions and 1 PhD grant available. whose topics support the project development. The research activities will naturally lead to academic publications (articles, books etc.), as well as participation in conferences. At least four workshops and one larger event are planned between 2024 and 2028.Efforts will be made towards developing intellectual property with possible patenting procedures.