Related papers: Unravelling Abstract Cyclic Proofs into Proofs by …
Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in…
A recent strand of research in structural proof theory aims at exploring the notion of analytic calculi (i.e. those calculi that support general and modular proof-strategies for cut elimination), and at identifying classes of logics that…
Contemporary proof assistants such as Coq require that recursive functions be terminating and corecursive functions be productive to maintain logical consistency of their type theories, and some ensure these properties using syntactic…
Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…
The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.