Related papers: On first-species counterpoint theory

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

We extend Mazzola's counterpoint model using category theory, generalizing from the category $\mathbf{Set}$ to other topoi with suitable properties. This generalization suggests that counterpoint's essential structure depends on specific…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…

This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation. We focus on showing…

This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…

We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the…

Our approach is basically a coherence approach, but we avoid the well-known pitfalls of coherence theories of truth. Consistency is replaced by reliability, which expresses support and attack, and, in principle, every theory (or agent,…

These notes contain a brief introduction to rational homotopy theory: its model category foundations, the Sullivan model and interactions with the theory of local commutative rings.

We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel,…

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…

In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by this author, Alexei G. Myasnikov and Francis Oger, we call…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…

In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…

Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…

To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…