Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Consolidation of Belief in Two Logics of Evidence

Recently, several logics have emerged with the goal of modelling evidence in a more relaxed sense than that of justifications. Here, we explore two of these logics, one based on neighborhood models and the other being a four-valued modal logic. We establish grounds for comparing these logics, finding, for any model, a counterpart in the other logic which represents roughly the same evidential situation. Then we propose operations for consolidation, answering our central question: What should the doxastic state of a rational agent be in a given evidential situation? These operations map evidence models to Kripke models. We then compare the consolidations in the two logics, finding conditions under which they are isomorphic. By taking this dynamic perspective on belief formation we pave the way for, among other things, a study of the complexity, and an AGM-style analysis of rationality of these belief-forming processes

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Persuasive argumentation and epistemic attitudes

These slides present the main notions and results of a work under construction that was presented in the 2nd DaLí Workshop, Dynamic Logic: New Trends and Applications in Porto, 9 October, 2019 and later published in the Lectures Notes in Computer Science (vol 12005). The work develops a formal study of persuasive dialogues among individuals, taking into account the epistemic attitudes of the involved agents. Abstract argumentation and dynamic epistemic logic provide the necessary tools for such an analysis. The interested reader is referred to the paper for further detailsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Гибридная интегральная схема для обработки звукового сигнала

Разработана гибридная интегральная схема с номинальным напряжением питания 1,4 В, током потребления 0,7 мА и габаритными размерами 8x4x3 мм для обработки звукового сигнала в автономной аппаратуре.Розроблена гібридна інтегральна схема з номінальною напругою живлення 1,4 В, струмом споживання 0,7 мА і габаритними розмірами 8x4x3 мм забезпечує багатофункціональну обробку звуковою сигналу в аналоговій мікроелектронній апаратурі. Наведено її конструкторсько-технологічні та електричні параметри.Developed hybrid integrated circuit with rated supply voltage of 1,4 V, current consumption 0,7 mA and overall dimensions 8x4x3 mm provides soft processing of the audio signal in analog microelectronic equipment. Given its design, technological and electrical parameters

Weakly Aggregative Modal Logic: Characterization and Interpolation

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation