Related papers: Dependent choice as a termination principle

Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of this form. It…

We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…

Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…

We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…

We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…

In this preliminary note, we will illustrate our ideas on automated mechanisms for termination and non-termination reasoning.

One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…

In this article, I develop a formal model of free will for complex systems based on emergent properties and adaptive selection. The model is based on a process ontology in which a free choice is a singular process that takes a system from…

We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…

While methods of code abstraction and reuse are widespread and well researched, methods of proof abstraction and reuse are still emerging. We consider the use of dependent types for this purpose, introducing a completely mechanical approach…

We give a new proof of the decidability of reachability in alternating pushdown systems, showing that it is a simple consequence of a cut-elimination theorem for some natural-deduction style inference systems. Then, we show how this result…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…

Termination is a central property in sequential programming models: a term is terminating if all its reduction sequences are finite. Termination is also important in concurrency in general, and for message-passing programs in particular. A…

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…

We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalising the groupoid model of type theory. As an application, we show that countable choice cannot be…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…