Probabilistic extensions for fragments of first-order logic

• Grant number: 16/25928-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2017
• End date: January 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
• Principal Investigator: Fabio Gagliardi Cozman
• Grantee: Glauber de Bona
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Probabilistic logic is at the intersection of the deductive and the inductive ways of reasoning and is one of the approaches to handling uncertainty in artificial intelligence. The most common probabilistic logics are propositional, lacking the power to deal with objects and predicates, which requires a first-order logic. Nevertheless, embedding probabilities into classical first-order logic typically yields formalisms with prohibitive computability and computational complexity. In order to circumvent that, one can endow a tractable first-order logic fragment with probabilistic operators. For instance, descriptive logics form a well-known family of first-order logic fragments with applicability to real-world problems. Even though a number of proposals in the literature have tackled probabilistic extensions of first-order logic fragments, there is no sistematic study of these formalisms. Due to the myriad of first-order logic fragments and to the different paths to enriching them with probabilistic reasoning, there is a vast spectrum of such formal systems yet to be explored, some of which possibly allowing practical application. This project aims at developing a formal framework to classify probabilistic extensions of classical first-order logic fragments, analysing their expressivity and computational complexity. This will lead to a better understanding of the mutual relation between these two aspects, which shall be accompanied by the formulation of new logics with practical application. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DE FARIA, FRANCISCO H. O. VIEIRA; GUSMAO, ARTHUR COLOMBINI; DE BONA, GLAUBER; MAUA, DENIS DERATANI; COZMAN, FABIO GAGLIARDI. Speeding up parameter and rule learning for acyclic probabilistic logic programs. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, v. 106, p. 32-50, MAR 2019. (17/19007-6, 16/18841-0, 16/25928-4, 16/01055-1, 15/21880-4)

DE BONA, GLAUBER; COZMAN, FABIO G.. On the Coherence of Probabilistic Relational Formalisms. Entropy, v. 20, n. 4, APR 2018. (16/18841-0, 16/25928-4)