Below you can see a list of past talks at the Logic Seminar. For forthcoming talks, see the main page.

##### Thursday, November 24, 2022 (online)

Eugenio Omodeo (DMG, Università degli studi di Trieste)

Julia Robinson, existential definability, and Hilbert’s 10^{th} problem

**Abstract**: Julia Bowman Robinson put forward in 1952 her notions of *existential definability* and *exponential growth*, both regarding relations on natural numbers. She foresaw that one of the new century problems posed by David Hilbert in the year 1900 would be settled by singling out an exponential-growth, existentially definable relation. The problem in question called for an algorithm that would establish, for any given polynomial *P* with integer coefficients, whether the equation *P = 0* has integer solutions or not.

Julia Robinson’s outlook had a decisive influence in the research that led, almost twenty years later, to a proof of the algorithmic unsolvability of Hilbert’s 10^{th} problem. She had designed from the outset a scheme for getting a specification of exponentiation in polynomial terms, out of any alike specification of an exponential-growth relation. In a 1969 paper, she would propose an improved version of her reduction scheme, of which a possible further refinement shines through a 1975 paper that she wrote in collaboration with Yuri V. Matiyasevich.

By retracing the stages of Julia Robinson’s contribution to the existential definition of exponentiation, this seminar does not simply intend to pay homage to an outstanding scientist. From an in-depth revisitation of her studies on Hilbert’s 10^{th}, along with the contributions of Martin Davis and Yuri Matiyasevich, a novel characterization of a key concept in computability might emerge: that of a *listable *set.

##### Thursday, November 17, 2022

Marian Călborean (University of Bucharest)

A notational extension of classical first-order logic to deal with vague language

**Abstract**: Vague language is treated as statistical dispersion, using the interplay of preference relations and monadic predicates. A notational extension of classical first-order logic allows defining a tolerant and a strict predicate for each monadic predicate. Results include the failure of weak non-contradiction and of a weak law of excluded middle, and the validity of weak tolerance principles. The logic proposed is compared to other order-sorted logics.

##### Thursday, November 10, 2022

Andrea Sgarro (DMG University of Trieste)

Possibility theory and the arithmetic of fuzzy numbers

**Abstract**: Taking inspiration from the seminal work in probability theory by A. N. Kolmogorov and H. R. Pitt, we intend to lay a sound foundation for fuzzy arithmetic, which is based on possibility theory beside fuzzy logic. A possibilistic interpretation of fuzzy arithmetic has long been known, however without taking it to its full consequences: in this paper we stress the basic role of the two limit-cases of possibilistic interactivity, namely deterministic equality versus non-interactivity, thus getting rid of weak points which have so far enfeebled more traditional approaches to fuzzy arithmetic.

##### Thursday, November 3, 2022

Bogdan Macovei (University of Bucharest)

Lean-certified Dynamic Epistemic Logic with Actions for Security Protocols

**Abstract**: We define a complete system of epistemic propositional dynamic logic with actions, that is fully defined and certified with the proof assistant Lean. Within our system, we specify security protocols as sequence of actions and we use epistemic reasoning for analyzing their properties.

##### Thursday, October 20, 2022

Mihai Prunescu (University of Bucharest & IMAR)

On a theorem of Gallai and related questions

**Abstract**: A theorem was stated by Tibor Gallai without proof and was later proven by several authors, in particular E. Witt or R. Rado. The theorem says that for every *k*-coloring of ℤ^{n} and every finite subset *F*⊆ℤ^{n}, there exists a homothetic image of *F* which is monochrome. This fact suggests various ultimately unsolvable sequences of SAT instances.