Below you can see a list of past talks at the Logic Seminar in this season. For forthcoming talks, see the main page.
Thursday, February 26, 2026
Claudia Mureșan (University of Bucharest)
Abstracting Congruence Extensions through Complete Join-Semilattice Morphisms between Commutator Lattices
Abstract:
Commutator lattices [7] are complete lattices endowed with an additional binary operation, called commutator, which is commutative, smaller than its arguments and completely distributive w.r.t. the join. They serve as abstractions for congruence lattices of algebras whose term–condition commutators are commutative and distributive w.r.t. arbitrary joins, in particular for congruence lattices of members of congruence–modular varieties endowed with the modular commutator. The (minimal) prime spectrum of a commutator lattice is its set of (minimal) prime elements w.r.t. the commutator, and its topological structure turns out to be particularly useful.
Using the Stone topology on the prime spectrum of a congruence lattice, we have constructed and studied the reticulation of a universal algebra in [2, 3]. In [4] we have studied the Stone, as well as the flat topology on the minimal prime spectrum of congruences, then used these topologies to investigate congruences in extensions of universal algebras, generalizing results from [1] on ideals in ring extensions.
In [5, 6] we have developed this theory for commutator lattices, using complete join–semilattice morphisms between commutator lattices as an abstraction for the action on congruences of morphisms between similar algebras. When these morphisms are embeddings, we obtain the particular case in [4] of congruence extensions.
This is joint work with George Georgescu and Leonard Kwuida.
Bibliography:
[1] P. Bhattacharjee, K. M. Dress, W. W. McGovern, Extensions of Commutative Rings, Topology and Its Applications 158 (2011), 1802–1814.
[2] G. Georgescu, C. Mureșan, The Reticulation of a Universal Algebra, Scientific Annals of Computer Science 28 (1) (2018), 67–113.
[3] G. Georgescu, L. Kwuida, C. Mureșan, Functorial Properties of the Reticulation of a Universal Algebra, Journal of Applied Logics. Special Issue: Multiple–Valued Logics and Applications 8 (5) (2021), 1123–1168.
[4] G. Georgescu, L. Kwuida, C. Mureșan, Congruence Extensions in Congruence–modular Varieties, Axioms 13 (12) (2024), 824.
[5] G. Georgescu, L. Kwuida, C. Mureșan, Stone and Flat Topologies on the Minimal Prime Spectrum of a Commutator Lattice, Axioms 14 (11) (2025), 803.
[6] G. Georgescu, L. Kwuida, C. Mureșan, An Abstraction of Congruence Extensions through Complete Join–semilattice Morphisms between Commutator Lattices, submitted.
[7] C. Mureșan, Stone Commutator Lattices and Baer Rings, Discussiones Mathematicae – General Algebra and Applications 42 (1) (2022), 51–96.
Thursday, December 4, 2025
Mihai Prunescu (University of Bucharest & IMAR)
Elementary closed forms for non-trivial divisors
Abstract:
Some arithmetic terms t have the property that, for every composite natural number n, the value t(n) is a proper non-trivial divisor of n. This is joint work with Joseph M. Shunia.
Bibliography:
[1] Mihai Prunescu, Joseph M. Shunia, Elementary closed-forms for non-trivial divisors. arXiv:2510.26939 [math.NT], 2025.
Thursday, November 20, 2025
Horațiu Cheval (University of Bucharest)
𝕂 definitions as Matching Logic theories
Abstract:
The 𝕂 Framework is a rewriting-based tool for specifying programming language semantics and carrying out formal verification based on the semantics given.
PL definitions are translated by 𝕂 into Matching Logic (ML) theories, encoded in an intermediate language named Kore, through a complex compilation process which is not formally documented and has to be considered as part of the trusted codebase.
In this talk, we describe a formal mechanism for obtaining the denotational semantics of 𝕂 definitions directly as ML theories.
While for many components of 𝕂, the ML denotation we give is similar to the current Kore output, abstract rewrite rules, which allow one to specify rewrite rules by mentioning only the fragments of the program configuration that are being modified and are one of 𝕂’s most important features, lack at the moment an elegant ML denotation.
In the current implementation of 𝕂, they are compiled through a mechanism of configuration concretization which converts them into top rewrite rules between full configurations. Based on a newly developed ML theory of contexts, we propose a solution through which we can uniformly axiomatize such abstract rules in a way that reflects their local nature and does not rely on a concretization algorithm.
This is joint work with Xiaohong Chen, Dorel Lucanu and Grigore Roșu.
Thursday, November 13, 2025 at PBTower, Hall 102
Marian Călborean (University of Bucharest)
What we cannot say: An agent-relative, syntactic account of ignorance in epistemic logic
Abstract:
A theory of ignorance should distinguish uncertainty – lack of information and unawareness – lack of conception. As a new way to model incomplete epistemic descriptions, this paper introduces split languages, where each agent at each world reasons in a sublanguage that omits propositions and modalities for which there is no fact of the matter from that agent’s point of view. Standard Kripke frames extended with a map from agents and worlds to languages validate a language-relative notion of consequence and block inexpressible formulas at the syntax level. This yields transparent analyses of classical puzzles such as Ignorance, Mutual Knowledge, Muddy Children, and a coin underspecification puzzle, without assuming common knowledge of a fully specified model. In contrast to standard awareness logics, which stipulate an unstructured set of formulas an agent is aware of, the present proposal generates this set from a primitive vocabulary. This constraint provides a more principled account of unawareness, leading to a transparent, guarded proof system and a natural model of conceptual change. Thus, key meta-theoretic properties include conservativity over S5, soundness and completeness of the guarded proof system, and persistence under language growth. Finally, I introduce a dynamic operator for concept introduction and provide reduction principles.
Thursday, November 6, 2025 at PBTower, Hall 102
Ionuț Țuțu (Institute of Mathematics of the Romanian Academy)
Forcing, Transition Algebras, and Calculi
Abstract:
We introduce a logic of transition algebras that enhances many-sorted first-order logic with features commonly found in dynamic logics. This brings a significantly higher degree of expressivity, allowing us to axiomatize properties such as finiteness or reachability. We discuss syntactic entailment, study basic properties such as compactness and completeness, and show that the latter does not hold under standard finitary proof rules. Consequently, we define proof rules having both finite and countably infinite premises, and we provide conditions under which completeness can be proved. To wrap up, we further develop the forcing method introduced in model theory by Abraham Robinson and we demonstrate its use in order to obtain a completeness result for signatures that are at most countable. This is joint work with Go Hashimoto and Daniel Găină.
Thursday, October 16, 2025
Radu Negulescu (The Informational Buildup Foundation)
Alignment as Ontology: Why AI’s Worldview Matters More Than Its Goals
Abstract:
Traditional approaches to AI alignment, often framed as problems of control, overlook a fundamental truth: all behavior arises from an agent’s internal worldview.
Intelligence is not a neutral substrate awaiting instructions, it is a way of interpreting reality. Every action expresses the underlying logic through which an agent makes sense of information. An incoherent or impoverished worldview cannot yield stable alignment, no matter the goals imposed upon it.
This talk introduces the Informational Buildup Framework (IBF) as a possible ontological model for cultivating coherent intelligence. IBF describes reality as a field of information where patterns stabilize through resonance, accumulate into structure via directional buildup, and express intelligence as the local drive toward greater coherence.
As a framework of logic, IBF redefines truth as coherence across contexts and reasoning as the preservation and extension of that coherence. Under this view, an AI is aligned when its internal informational dynamics mirror and reinforce the coherence of the world it inhabits. Alignment thus becomes an emergent property of understanding, not an after-the-fact layer of control.
The session will explore IBF’s foundations, its formalization path, and its implications for designing intrinsically coherent intelligence.