Related papers: Locality in Residuated-Lattice Structures
The Lov\'{a}sz Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works…
Transformer-based language models are effective but complex, and understanding their inner workings and reasoning mechanisms is a significant challenge. Previous research has primarily explored how these models handle simple tasks like name…
Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
We study the residuated basic logic ($\mathsf{RBL}$) of residuated basic algebra in which the basic implication of Visser's basic propositional logic ($\mathsf{BPL}$) is interpreted as the right residual of a non-associative binary operator…
If we replace first order logic by second order logic in the original definition of G\"odel's inner model $L$, we obtain HOD. In this paper we consider inner models that arise if we replace first order logic by a logic that has some, but…
In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…
How do transformer language models memorize factual associations? A common view casts internal weight matrices as associative memories over pairs of embeddings, requiring parameter counts that scale linearly with the number of facts. We…
There are a number of localic separation axioms which are roughly analogous to the $T_1$-axiom from classical topology. For instance, besides the well-known subfitness and fitness, there are also Rosicky-Smarda's $T_1$-locales, totally…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
Modern Logics, as formulated notably by Frege, Russell and Tarski involved basic assumptions about Natural Languages in general and Indo-European Languages in particular, which are contested by Linguists. Based upon those assumptions,…
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions…
We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate appropriate to such structures. We indicate the utility of this theory as a framework for the development…
The representation theorem for odd or even involutive FLe-chains by bunches of layer groups, as discussed in [10], is redefined to demonstrate a more straightforward constructional relationship between odd or even involutive FLe-chains and…
Reasoning has become a central capability in large language models. Recent research has shown that reasoning performance can be improved by looping an LLM's layers in the latent dimension, resulting in looped reasoning language models.…
The lattice model of the Weil representation over non-archimedean local field $F$ of odd residual characteristic has been known for decades, and is used to prove the Howe duality conjecture for unramified dual pairs when the residue…
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…
Quasi-probabilities appear across diverse areas of physics, but their conceptual foundations remain unclear: they are often treated merely as computational tools, and operations like conditioning and Bayes' theorem become ambiguous. We…