Swiss Logic Gathering 2024

The Swiss Logic Gathering 2024 will take place on December 13 in the seminar room ExWi 228 of the Exakte Wissenschaft Building (ExWi) at the University of Bern.

Schedule

Abstracts

In this talk I will present various results that can be obtained using weak bisimulations for the interpretability logic with respect to Verbrugge semantics. Verbrugge semantics is a generalization of the basic Veltman semantics for interpretability logic, which turned out to possess various good properties. It is proved that with the standard definition of bisimulation for Verbrugge semantics that has been used so far in the literature, the analogs of some results for Veltman semantics do not hold in the case of Verbrugge semantics. Therefore, a new version of bisimulation, called weak bisimulation, was given in [1]. Among the more important results that we can obtain by using weak bisimulations (and corresponding weak bisimulation games), I will present the result that n-modal equivalence implies weak bisimulation, the property of finite models, and van Benthem's characterization theorem with respect to Verbrugge semantics.

References:
[1] S. Horvat, T. Perkov, M. Vuković, Bisimulations and bisimulation games for Verbrugge semantics, Mathematical Logic Quarterly 69(2023), 231-243

Let \(\lambda\) be an uncountable cardinal such that \( 2^{< \lambda } = \lambda \). Working in the setup of generalized descriptive set theory, we study the structure of \( \lambda^+ \)-Borel measurable functions with respect to various kinds of limits, and isolate a suitable notion of \( \lambda \)-Baire class \( \xi \) function. Among other results, we provide higher analogues of two classical theorems of Lebesgue, Hausdorff, and Banach, namely:

1. A function is \( \lambda^+ \)-Borel measurable if and only if it can be obtained from continuous functions by iteratively applying pointwise \( D \)-limits, where \( |D| \leq \lambda \).
2. A function is of \( \lambda \)-Baire class \( \xi \) if and only if it is \( \lambda^+\)-\(\boldsymbol{\Sigma}^{0}_{\xi+1} \)-measurable.

I point out a critical subjective Gödelian loophole in the Swiss Constitution, namely its Article 190, whose authoritative interpretation I prove to be a misinterpretation. In Swiss legislation, jurisprudence, and jurisdiction (thus de jure and de facto, respectively), this loophole has enabled the abuse of elementary logic and—a fortiori—fundamental law (the violation of sacrosanct human rights), and thus the systematic miscarriage of legislation (anti-constitutional law) and justice (anti-democratic rule of law). This malpractice has happened through the false pretence that the article be non-self-applicable and thus that the Swiss Constitution be irrelevant to the corpus of (anti-constitutional) federal law (to be derived if not deduced from the Constitution) to the point of posing a critical threat to the Swiss nation-state. Luckily, the loophole turns out to be objectively (logically and thus legally) self-mending (by self-application) and thus the Constitution to be self-amending (under correct interpretation).

We introduce an intuitionistic analogue of monotone modal logic. The logic is obtained by taking a first-order perspective on classical monotone modal logic and then moving to an intuitionistic first-order setting. This is similar to Simpsons approach to intuitionistic (normal) modal logic. We axiomatize the logic and give a sound and complete neighbourhood-style semantics.