Related papers: Dependent choice as a termination principle
It is argued that the concept of free will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two-stage model, which deconstructs free…
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces,…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…
Based on the principle of causality, I advance a new principle of variation and try to use it as the most general principle for research into laws of nature.
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Providing users with alternatives to choose from is an essential component in many online platforms, making the accurate prediction of choice vital to their success. A renewed interest in learning choice models has led to significant…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
This paper is an expository contribution reporting on published work. It focusses on an approach followed in the rewriting community to formalize the concept of strategy. Based on rewriting concepts, several definitions of strategy are…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…
This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the…
We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the \emph{use criterion}, according to which in order for some premises to have some…
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
More and more processes governing our lives use in some part an automatic decision step, where -- based on a feature vector derived from an applicant -- an algorithm has the decision power over the final outcome. Here we present a simple…