Related papers: On first-species counterpoint theory
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
This paper presents a model of contrastive explanation using structural casual models. The topic of causal explanation in artificial intelligence has gathered interest in recent years as researchers and practitioners aim to increase trust…
We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
Counterfactual reasoning -- envisioning hypothetical scenarios, or possible worlds, where some circumstances are different from what (f)actually occurred (counter-to-fact) -- is ubiquitous in human cognition. Conventionally,…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
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…
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…
We extend the notion of type sequence to rings that are not necessarily residually rational. Using this invariant we characterize different types of rings as almost Gorenstein rings and rings of maximal length.
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…
We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…
Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby identify and discover 'types': of behaviour, views,…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
In this paper we examine the natural interpretation of a ramified type hierarchy into Martin-L\"of type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of…
We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…