相关论文: Remarks on Primitive Regulation

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

Let $\xx= x_1,\ldots,x_r$ denote a system of elements of a commutative ring $R$. For an $R$-module $M$ we investigate when $\xx$ is $M$-pro-regular resp. $M$-weakly pro-regular as generalizations of $M$-regular sequences. This is done in…

The noise-type completion C of a noise-type Boolean algebra B is generally not the same as the closure of B. As shown in Part I (Introduction, Theorem 2), C consists of all complemented elements of the closure. It appears that C is the…

We introduce incongruent normal form (INF), a structural representation for self-referential semantic sentences. An INF replaces a self-referential sentence with a finite family of non-self-referential sentences that are individually…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

Let $G$ be a finite group. Let $K/k$ be a Galois extension of number fields with Galois group isomorphic to $G$, and let $C \subseteq \mathrm{Gal}(K/k) \simeq G$ be a conjugacy invariant subset. It is well known that there exists an…

In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure of a boolean relation (a set of boolean vectors) by…

Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…

Let $\mathcal C$ be a class of modules and $\mathcal L = \varinjlim \mathcal C$ the class of all direct limits of modules from $\mathcal C$. The class $\mathcal L$ is well understood when $\mathcal C$ consists of finitely presented modules:…

Even if binary relations and orders are a common formalization topic, we need to formalize specific orders (namely monomial and graded) in the process of formalizing in Rocq the finite element method. This article is therefore definitions,…

We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that…

This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter…

We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to…

Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…

If C and D are varieties of algebras in the sense of general algebra, then by a representable functor C --> D we understand a functor which, when composed with the forgetful functor D --> Set, gives a representable functor in the classical…

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

Let L be a nonunimodular definite lattice. Using a theorem of Elkies we show that whether L embeds in the standard definite lattice of the same rank is completely determined by a collection of lattice correction terms, one for each…

In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a…

Here, we present a subcategory pEff of Hyland's Effective Topos Eff which can be considered a predicative variant of Eff itself. The construction of pEff is motivated by the desire of providing a "predicative" categorical universe of…

The sequential form of a statement $\forall\xi(B(\xi) \rightarrow \exists\zeta A(\xi,\zeta))$ is the statement $\forall\xi(\forall n B(\xi_n) \rightarrow \exists\zeta \forall n A(\xi_n,\zeta_n))$. There are many classically true statements…