Related papers: Unravelling Abstract Cyclic Proofs into Proofs by …
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The…
We study the logical complexity of proofs in cyclic arithmetic ($\mathsf{CA}$), as introduced in Simpson '17, in terms of quantifier alternations of formulae occurring. Writing $C\Sigma_n$ for (the logical consequences of) cyclic proofs…
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions to normal forms, and employ them to construct cubical…
Cyclic models of the universe have the advantage of avoiding initial conditions problems related to postulating any sort of beginning in time. To date, the only known viable examples of cyclic models have been ekpyrotic. In this paper, we…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
Typically, real-world stochastic processes are not easy to analyze. In this work we study the representation of any stochastic process as a memoryless innovation process triggering a dynamic system. We show that such a representation is…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
The two-way modal mu-calculus is the extension of the (standard) one-way mu-calculus with converse (backward-looking) modalities. For this logic we introduce two new sequent-style proof calculi: a non-wellfounded system admitting infinite…
A cyclic proof system, called CLKID-omega, gives us another way of representing inductive definitions and efficient proof search. The 2005 paper by Brotherston showed that the provability of CLKID-omega includes the provability of LKID,…
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
Relying on work of Kashiwara-Schapira and Schmid-Vilonen, we describe the behaviour of characteristic cycles with respect to the operation of geometric induction, the geometric counterpart of taking parabolic or cohomological induction in…
In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…