Related papers: Proofs and surfaces
Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
In a recent paper, Herbelin developed a calculus dPA$^\omega$ in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of…
Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…
We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…
We consider a Dirichlet series $\sum_{n=1}^{\infty}a_n^{-s}$, where $a_n$ satisfies a linear recurrence of arbitrary degree with integer coefficients. Under suitable hypotheses, we prove that it has a meromorphic continuation to the complex…
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
The work is devoted to constructing a wide class of differential-functional dynamical systems, whose rich algebraic structure makes their integrability analytically effective. In particular, there is analyzed in detail the operator Lax type…
This paper describes a formalism that subsumes Peterson's intermediate quantifier syllogistic system, and extends the ideas by van Eijck on Aristotle's logic. Syllogisms are expressed in a concise form making use of and extending the…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
The basic concepts underlying our analysis of {\it W-algebras} as extended symmetries of integrable systems are summarized. The construction starts from the second hamiltonian structure of ``Generalized Drinfel'd-Sokolov'' hierarchies, and…
We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the…
Recently introduced Petri net-based formalisms advocate the importance of proper representation and management of case objects as well as their co-evolution. In this work we build on top of one of such formalisms and introduce the notion of…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
Right-linear (or left-linear) grammars are a well-known class of context-free grammars computing just the regular languages. They may naturally be written as expressions with (least) fixed points but with products restricted to letters as…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
We introduce a framework for ordinal notation systems, present a family of strong yet simple systems, and give many examples of ordinals in these systems. While much of the material is conjectural, we include systems with conjectured…
We introduce a dynamical Mordell-Lang-type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this…
Formal reasoning about inductively defined relations and structures is widely recognized not only for its mathematical interest but also for its importance in computer science, and has applications in verifying properties of programs and…