|
Published: 31st December 2024 DOI: 10.4204/EPTCS.415 ISSN: 2075-2180 |
Non-Classical Logics. Theory and Applications (NCL) is an international conference aimed at presenting novel results and survey works in widely understood non-classical logics and their applications. It was initially held in Łódź, Poland, in September 2008 and 2009. Later on, it was organised alternately in Toruń (2010, 2012, 2015, 2018) and Łódź (2011, 2013, 2016, 2022). The tenth edition of the Conference, organised by the University of Lodz in 2022, was the first one with the Proceedings published in EPTCS. We have a great honour and pleasure to continue this practice and for the second time include all accepted long papers in an EPTCS volume.
This 11th edition is supported by the European Research Council as one of the events organised within the project ExtenDD. In addition to 4 invited talks and 18 contributed talks, we accepted 18 short presentations on the basis of a light reviewing process. This year's edition of NCL was also co-located with the 9th edition of the Workshop on connexive logics and its program included a special session devoted to the presentation of recent results obtained within the project ExtenDD. The conference website can be found at
The Program Committee received about 30 high-quality submissions, which were evaluated on the basis of their significance, novelty and technical correctness. Reviewing was single-blind and each paper was subjected to at least two independent reviews, followed by a thorough discussion within the Program Committee. 18 submissions were selected for presentation on the basis of their quality. This volume contains abstracts of the invited talks and full versions of the accepted submissions.
The Program Committee offered two awards for outstanding submissions. The Best Paper Award went toThe awards have been financially supported by Springer Nature.
We would like to thank all the people who contributed to the successful performance of NCL'24. In particular, we thank the invited speakers for their talks, the authors for their contributed papers and inspiring presentations, the organisers and participants of the workshop, and all participants for their attendance and discussions. We thank the members of the Program Committee and external reviewers for their careful and competent reviewing.
We also greatly appreciate the financial support of the European Research Council, the University of Lodz, and Springer Nature. Last but not least, one of our invited speakers, professor Hanamantagouda P. Sankappanavar, has covered the costs of travel and accommodation for one of the participants of NCL'24.
In the first half of my talk, I will introduce five "unorthodox" algebras, four of which have 3-element chain as a lattice-reduct and the fifth one has a 4-element Boolean lattice as a lattice-reduct. These algebras are anti-Boolean and yet have some amazing similarities with Boolean algebras. I develop an algebraic theory of these algebras that leads to an equational axiomatization of the variety 𝕌ℕ𝕆1 generated by the five unorthodox algebras. I, then, look at the structure of the lattice of subvarieties of the variety 𝕌ℕ𝕆1 and provide bases for all 32 subvarieties of 𝕌ℕ𝕆1. I also indicate why these algebras collectively generate a discriminator variety and individually are primal algebras.
In the second half, I will introduce an algebraizable logic (in the sense of Blok and Pigozzi) called "𝒰𝒩𝒪1" whose equivalent algebraic semantics is the variety 𝕌ℕ𝕆1. Here I rely on the well-known results of Rasiowa on implicative logics and of Blok and Pigozzi on algebraizability. I will then present axiomatizations for all the axiomatic extensions of 𝒰𝒩𝒪1 and discuss decidability of these logics.
This talk explores global proof transformations within sequent and hypersequent calculi. These transformations result in:
CEGAR-tableaux utilise SAT-solvers and modal clause learning to give the current state-of-the-art satisfiability checkers for basic modal logics K, KT and S4. I will start with a brief overview of the basic CEGAR-tableaux method for these logics.
I will show how to extend CEGAR-Tableaux to handle the five basic extensions of K by the axioms D, T, B, 4 and 5, and then indirectly to the whole modal cube. Experiments confirm that the resulting satisfiability-checkers are also the current best ones for these logics.
I will show how to extend CEGAR-tableaux to handle the modal tense logic Kt, which involves modalities for the "future" and the "past". Once again, our experiments show that CEGAR-tableaux are state-of-the-art for these logics.
The talk is intended as an exposition for a broad audience and does not require any knowledge of SAT-solvers or computer science but some knowledge of modal logic would help.
This work is on using formal logic for capturing reasoning about strategic abilities of rational agents and groups (coalitions) of agents to guarantee achievement of their goals, while acting and interacting within a society of agents. That strategic interaction can be quite complex, as it usually involves various patterns combining cooperation and competition.
The earliest logical systems for formalizing strategic reasoning include Coalition Logic (CL) introduced and studied by Pauly in the early 2000s and the independently introduced and studied at about the same period by Alur, Henzinger and Kupferman Alternating Time Temporal Logic ATL.
Recently more expressive and versatile logical systems, capturing the reasoning about strategic abilities of socially interacting rational agents and coalitions, have been proposed and studied, including:
Paper [1] provides a recent overview of these.
[1] Valentin Goranko (2023): Logics for Strategic Reasoning of Socially Interacting Rational Agents: An Overview and Perspectives. Logics 1(1), pp. 4–35, doi:10.3390/logics1010003. Available at https: //www.mdpi.com/2813-0405/1/1/3.