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Tomasz Kowalski

Publications and source records attributed to Tomasz Kowalski.

At least 19 recordsLinked to original sources
arXiv2026

A generic construction of free algebras in varieties of Hilbert algebras and Brouwerian semilattices

We give a generic construction of the n-generated free Hilbert algebras and Brouwerian semilattices by a uniform method applicable to any variety of Hilbert algebras or Brouwerian semilattices, as long as a manageable description of subdirectly irreducible algebras in that variety is available. A slight modification yields analogous constructions for varieties of Hilbert algebras and Brouwerian semilattices with zero. As examples we construct free algebras in varieties of bounded height and of bounded width; we also find a closed formula for the free spectrum of linear Hilbert algebras. Finally, we obtain a few results on structural completeness of varieties of Hilbert algebras with zero, in particular, we give a sufficient condition for a quasi-equation to be equivalent to an equation.

math.LO↗
arXiv2026

Definable Classes of Models and Frames in Bi-intuitionistic Logic

The question of the expressive power of a given logical language with Kripke relational semantics has at least two dimensions: (1) what the language can say about frames, and (2) what it can say about models. The Goldblatt-Thomason theorem provides a model-theoretic characterisation of modal axiomatisability for elementary classes of frames in terms of closure under taking generated subframes, disjoint unions, bounded morphic images, and reflection of ultrafilter extensions. Goldblatt also provides a similar characterisation for axiomatisability in intuitionistic logic of classes of models rather than frames. In this article we provide analogous results for bi-intuitionistic logic, a natural expressive extension of intuitionistic logic obtained by adding a binary connective dual to the intuitionistic implication, introduced in the 1970s independently by Dieter Klemke and Cecylia Rauszer. Together with previous results, such as a van Benthem bisimulation characterisation theorem and a Lindstrom theorem, this provides a complete picture of the expressive power of propositional bi-intuitionistic logic.

math.LO↗
arXiv2025

Beyond wreath and block

We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element flip-flop monoid is replaced by the two-element semilattice.

math.GR↗
arXiv2025

Kites and representations of pseudo MV-algebras

We investigate the structure of perfect residuated lattices, focussing especially on perfect pseudo MV-algebras. We show that perfect pseudo MV-algebras can be represented as a generalised version of kites of Dvurečenskij and Kowalski, and that they are categorically equivalent to $\ell$-groups with a distinguished automorphism. We then characterise varieties generated by kites and describe the lattice of these varieties as a complete sublattice of the lattice of perfectly generated varieties of perfect pseudo MV-algebras.

math.LO↗
arXiv2025

Splittings in varieties of logic

We study splittings, or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the Non-Splitting Lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splittings algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double p-algebras the only splitting algebras are the two-element and three-element chains.

math.LO↗
arXiv2025

Hybrid-Dynamic Ehrenfeucht-Fraisse Games

Ehrenfeucht-Fraisse games provide means to characterize elementary equivalence for first-order logic, and by standard translation also for modal logics. We propose a novel generalization of Ehrenfeucht- Fraisse games to hybrid-dynamic logics which is direct and fully modular: parameterized by the features of the hybrid language we wish to include, for instance, the modal and hybrid language operators as well as first-order existential quantification. We use these games to establish a new modular Fraisse-Hintikka Theorem for hybrid-dynamic propositional logic and its various fragments. We study the relationship between countable game equivalence (determined by countable Ehrenfeucht- Fraisse games) and bisimulation (determined by countable back-and-forth systems). In general, the former turns out to be weaker than the latter, but under certain conditions on the language, the two coincide. We also use games to prove that for reachable image-finite Kripke structures elementary equivalence implies isomorphism.

cs.LO↗
arXiv2024

Quasivarieties of p-algebras: some new results

We investigate quasivarieties of (distributive) p-algebras. We sharpen some previous results, give a better picture of the subquasivariety lattice, and prove that quasivarieties generated by free p-algebras belong to a rather small quasivariety characterised by excluding all but 3 subdirectly irreducibles.

math.LO↗
arXiv2024

Decidable varieties of p-algebras

We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.

math.LO↗
arXiv2024

Response of the first POLAR-2 Prototype to Polarized Beams

POLAR-2 is a dedicated gamma-ray polarimeter currently foreseen to be launched towards the China Space Station around 2027. The design of the detector is based on the legacy of its predecessor mission POLAR which was launched in 2016. POLAR-2 aims to measure the polarization of the Gamma-ray Burst prompt emission within the 30-800 keV energy range. Thanks to its high sensitivity to gamma-ray polarization, as well as its large effective area, POLAR-2 will provide the most precise measurements of this type to date. Such measurements are key to improve our understanding of the astrophysical processes responsible for Gamma-Ray Bursts. The detector consists of a segmented array of plastic scintillator bars, each one of which is read out by a Silicon PhotoMultiplier channel. The flight model of POLAR-2 will contain a total of 6400 scintillators. These are divided into 100 groups of 64 bars each, in so-called polarimeter modules. In recent years, the collaboration has designed and produced the first prototypes of these polarimeter modules and subjected these to space qualification tests. In addition, in April 2023, the first of these modules were calibrated using fully polarized gamma-ray beams at the European Synchrotron Radiation Facility (ESRF) in France. In this work, we will present the results of this calibration campaign and compare these to the simulated performance of the POLAR-2 modules. Potential improvements to the design are also discussed. Finally, the measurements are used, in combination with the verified simulation framework, to estimate the scientific performance of the full POLAR-2 detector and compare it to its predecessor.

astro-ph.IM↗
arXiv2024

Free p-algebras revisited: an algebraic investigation of implication-free intuitionism

We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results, as well as a complete characterisation of structurally complete varieties of p-algebras.

math.LO↗
arXiv2023

A modular bisimulation characterisation for fragments of hybrid logic

There are known characterisations of several fragments of hybrid logic by means of invariance under bisimulations of some kind. The fragments include $\{\store, \jump\}$ with or without nominals (Areces, Blackburn, Marx), $\jump$ with or without nominals (ten Cate), and $\store$ without nominals (Hodkinson, Tahiri). Some pairs of these characterisations, however, are incompatible with one another. For other fragments of hybrid logic no such characterisations were known so far. We prove a generic bisimulation characterisation theorem for all standard fragments of hybrid logic, in particular for the case with $\store$ and nominals, left open by Hodkinson and Tahiri. Our characterisation is built on a common base and for each feature extension adds a specific condition, so it is modular in an engineering sense.

math.LO↗
arXiv2023

Proton irradiation of plastic scintillator bars for POLAR-2

POLAR-2, a plastic scintillator based Compton polarimeter, is currently under development and planned for a launch to the China Space Station in 2025. It is intended to shed a new light on our understanding of Gamma-Ray Bursts by performing high precision polarization measurements of their prompt emission. The instrument will be orbiting at an average altitude of 383 km with an inclination of 42° and will be subject to background radiation from cosmic rays and solar events. In this work, we tested the performance of plastic scintillation bars, EJ-200 and EJ-248M from Eljen Technology, under space-like conditions, that were chosen as possible candidates for POLAR-2. Both scintillator types were irradiated with 58 MeV protons at several doses from 1.89 Gy (corresponding to about 13 years in space for POLAR-2) up to 18.7 Gy, that goes far beyond the expected POLAR-2 life time. Their respective properties, expressed in terms of light yield, emission and absorption spectra, and activation analysis due to proton irradiation are discussed. Scintillators activation analyses showed a dominant contribution of $β^+$ decay with a typical for this process gamma-ray energy line of 511 keV.

astro-ph.IM↗
arXiv2022

Temperature dependence of radiation damage annealing of Silicon Photomultipliers

The last decade has increasingly seen the use of silicon photomultipliers (SiPMs) instead of photomultiplier tubes (PMTs). This is due to various advantages of the former on the latter like its smaller size, lower operating voltage, higher detection efficiency, insensitivity to magnetic fields and mechanical robustness to launch vibrations. All these features make SiPMs ideal for use on space based experiments where the detectors require to be compact, lightweight and capable of surviving launch conditions. A downside with the use of this novel type of detector in space conditions is its susceptibility to radiation damage. In order to understand the lifetime of SiPMs in space, both the damage sustained due to radiation as well as the subsequent recovery, or annealing, from this damage have to be studied. Here we present these studies for three different types of SiPMs from the Hamamatsu S13360 series. Both their behaviour after sustaining radiation equivalent to 2 years in low earth orbit in a typical mission is presented, as well as the recovery of these detectors while stored in different conditions. The storage conditions varied in temperature as well as in operating voltage. The study found that the annealing depends significantly on the temperature of the detectors with those stored at high temperatures recovering significantly faster and at recovering closer to the original performance. Additionally, no significant effect from a reasonable bias voltage on the annealing was observed. Finally the annealing rate as a function of temperature is presented along with various operating strategies for the future SiPM based astrophysical detector POLAR-2 as well as for future SiPM based space borne missions.

astro-ph.IM↗
arXiv2022

LLRF for PolFEL Accelerator

PolFEL stands for Polish Free Electron Laser, the first FEL research infrastructure in Poland. This facility is under development, and it will operate in three wavelength ranges: IR, THz and VUV, using different types of undulators. Machine will be driven by 200 MeV linear superconducting accelerator, which will operate in both, pulsed wave (PW) and continuous wave (CW) modes. This paper will describe the concept, current status and the first results of the LLRF systems development.

physics.acc-ph↗
arXiv2022

Proton Irradiation of SiPM arrays for POLAR-2

POLAR-2 is a space-borne polarimeter, built to investigate the polarization of Gamma-Ray Bursts and help elucidate their mechanisms. The instrument is targeted for launch in 2024 or 2025 aboard the China Space Station and is being developed by a collaboration between institutes from Switzerland, Germany, Poland and China. The instrument will orbit at altitudes between 340km and 450km with an inclination of 42$^{\circ}$ and will be subjected to background radiation from cosmic rays and solar events. It is therefore pertinent to better understand the performance of sensitive devices under space-like conditions. In this paper we focus on the radiation damage of the silicon photomultiplier arrays S13361-6075NE-04 and S14161-6050HS-04 from Hamamatsu. The S13361 are irradiated with 58MeV protons at several doses up to 4.96Gy, whereas the newer series S14161 are irradiated at doses of 0.254Gy and 2.31Gy. Their respective performance degradation due to radiation damage are discussed. The equivalent exposure time in space for silicon photomultipliers inside POLAR-2 with a dose of 4.96Gy is 62.9 years (or 1.78 years when disregarding the shielding from the instrument). Primary characteristics of the I-V curves are an increase in the dark current and dark counts, mostly through cross-talk events. Annealing processes at $25^{\circ}C$ were observed but not studied in further detail. Biasing channels while being irradiated have not resulted in any significant impact. Activation analyses showed a dominant contribution of $β^{+}$ particles around 511keV. These resulted primarily from copper and carbon, mostly with decay times shorter than the orbital period.

astro-ph.IM↗
arXiv2022

Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols

In the the present contribution, we prove an Omitting Types Theorem (OTT) for an arbitrary fragment of hybriddynamic first-order logic with rigid symbols (i.e. symbols with fixed interpretations across worlds) closed under negation and retrieve. The logical framework can be regarded as a parameter and it is instantiated by some well-known hybrid and/or dynamic logics from the literature. We develop a forcing technique and then we study a forcing property based on local satisfiability, which lead to a refined proof of the OTT. For uncountable signatures, the result requires compactness, while for countable signatures, compactness is not necessary. We apply the OTT to obtain upwards and downwards Löwenheim-Skolem theorems for our logic, as well as a completeness theorem for its constructor-based variant. The main result of this paper can easily be recast in the institutional model theory framework, giving it a higher level of generality.

math.LO↗