* Together with my supervisor, we characterize a new clausal-like form over the infinitely-valued propositional Lukasiewicz logic, LCNF. We prove this class of formulas is normal for SAT: this means that each (arbitrary) formula in the logic has an associated formula in the regular clausal form introduced such that each evaluation satisfies the former one if and only if it satisfies the latter. I have been able to introduce a finite resolution rule which is sound and complete for the infinitely-valued Lukasiewicz logic.
* In work I have done alone, I have proven that the restriction of several FO logics to their modal formulas (a regular form of the predicates logics, among which FO Lukasiewicz, Product, and a large family of others identified with certain conditions) is a fragment which is not axiomatizable (i.e. not recursively enumerable, so not in Sigma_1 from the AH). This is a very strong result that has come as a surprise, since the analogous fragment in classical logic is indeed axiomatizable and decidable. It points to the extreme complexity of these logics.
* Together with the project supervisor and other two researchers, we study reduction to clausal form of non-clausal MaxSAT and MinSAT to clausal MaxSAT and MinSAT. We present three different cost-preserving transformations and we report on an empirical comparison of the performance of the proposed transformations when solved with a state-of-the-art MaxSAT solver.
* Together with my supervisor and a colleague from the Czech Academy of Sciences, where we study different algorithms solving MAX-SAT in the real valued MV-algebra. We later define an alternative analytic method with preprocessing in terms of a Tseitin transformation of the input, followed by a reduction to a system of linear constraints, in analogy to the earlier approaches of Hähnle and Olivetti.
* In a work I have done alone, I have proven that the local modal fragment of the predicate Product logic is indeed decidable (hence in Δ_1 from the Arithmetical Hierarchy) even if its definition as a logic, based on valued Kripke models, requires of infinite models. The reduction of this question to a decidable problem is based on a codification of the infinitary information that I believe can have later uses in related questions.
OVERVIEW OF EXPLOITATION/DISSEMINATION
* 2 indexed already published journal paper publications (one of them in the top journal in general logic), 1 submitted journal publication under revision since June 2023 (
https://arxiv.org/abs/2306.13903(odnośnik otworzy się w nowym oknie)) 1 manuscript in latter stages of development to be submitted to a journal.
* 1 published article in indexed proceedings
* Participation as INVITED SPEAKER in 5 international conferences. Participation as contributed speaker (with peer review) in 3 international conferences.
