RESEARCH

Logic stands at the intersection of mathematics, computer science, and philosophy. It provides the formal language needed to analyze one of humanity’s defining traits: our capacity to reason.

Classical logic operates on a strict binary dichotomy of true or false. However, both artificial systems and human agents must regularly navigate incomplete, uncertain, graded, or context-dependent information. My research addresses these boundary conditions by developing the logical foundations of AI and formalizing the principles and limits of rationality.

My work spans three main interconnected tracks:

1. Graded Reasoning and Non-Classical Rationality

Human action, natural language, and rational discourse are saturated with graded properties that simple binary truth values cannot capture. I investigate many-valued logics, extending formal systems across propositional, modal, and predicate formalisms. From a philosophical and cognitive standpoint, these logics serve as essential formal models for reasoning with degree-based truth, vagueness, and uncertainty.

For further background, see the Stanford Encyclopedia entry on fuzzy logic or the three volumes of the Handbook of Mathematical Fuzzy Logic.

2. Foundations of AI and Databases 

Beyond pure philosophy, many-valued and algebraic framework provide critical tools for theoretical computer science. My contributions to AI and computational logic focus on expanding the semantics of computation and data manipulation, including:

• Many-Valued Finite Model Theory: Study of asymptotic zero-one laws in non-classical frameworks, showing that every sentence in a purely relational language is almost surely false or almost surely true, and proving that the complexity of determining the almost sure value of a given sentence is PSPACE-complete (generalizing Grandjean’s result for the classical case).

• Descriptive Complexity and Weighted Logics: Mapping models of computation to generalized logical specifications, we study descriptive complexity based on weighted Turing machines over arbitrary semirings, widely generalizing Fagin’s seminal result that characterized NP in terms of existential second-order logic.

• Automated Reasoning in Spatial and Temporal Multi-Modal Logics: Extending classical spatial and temporal logics to many-valued settings over finite algebras and developing analytic tableau-based reasoning systems to check graded satisfiability and validity, implemented and integrated into the open-source symbolic AI framework Sole.jl.

• Database Theory and Multidimensional Inference: Extending classical foundational results, such as generalizations of Codd’s Theorem, to complex query processing over databases annotated on semirings, as well as developing a multidimensional paradigm for many-valued reasoning.