Related papers: Cyclic and Inductive Calculi are equivalent

Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize this algorithm to constacyclic codes. As an application of the algorithm we…

This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational…

We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…

Reversible computation is key in developing new, energy-efficient paradigms, but also in providing forward-only concepts with broader definitions and finer frames of study.Among other fields, the algebraic specification and representation…

I argue that, on a judicious reading of two existing criteria--one syntactic and the other semantic--dual theories can be taken to be empirically equivalent. The judicious reading is straightforward, but leads to the surprising conclusion…

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…

We introduce the cyclic major index of a cycle permutation and give a bivariate analogue of enumerative formula for the cyclic shuffles with a given cyclic descent numbers due to Adin, Gessel, Reiner and Roichman, which can be viewed as a…

Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which…

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…

In this paper, we study Cyclic Henkin Logic CHL, a logic that can be described as provability logic without the third L\"ob condition, to wit, that provable implies provably provable (aka principle 4). The logic CHL does have full modalised…

Cyclic data structures, such as cyclic lists, in functional programming are tricky to handle because of their cyclicity. This paper presents an investigation of categorical, algebraic, and computational foundations of cyclic datatypes. Our…

We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…

This note describes a conjecture involving cyclotomic polynomials and some initial thoughts towards a solution. Given positive integers $m,n$, the conjecture is that either $\Phi_m(q)\leqslant\Phi_n(q)$ or $\Phi_m(q)\geqslant\Phi_n(q)$…

In the causal learning setting, we wish to learn cause-and-effect relationships between variables such that we can correctly infer the effect of an intervention. While the difference between a cyclic structure and an acyclic structure may…

In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…

Despite the success of chain of thought in enhancing language model reasoning, the underlying process remains less well understood. Although logically sound reasoning appears inherently crucial for chain of thought, prior studies…

Notions of asimulation and k-asimulation introduced in [Olkhovikov, 2011] are extended onto the level of predicate logic. We then prove that a first-order formula is equivalent to a standard translation of an intuitionistic predicate…

We prove that the Calabi invariant of a $C^1$ pseudo-rotation of the unit disk, that coincides with a rotation on the unit circle, is equal to its rotation number. This result has been shown some years ago by Michael Hutchings (under very…

We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…

This paper proposes first-order modal $\xi$-calculus as well as genealogical Kripke models. Inspired by modal $\mu$-calculus, first-order modal $\xi$-calculus takes a quite similar form and extends its inductive expressivity onto a…