Related papers: Towards a formalization of budgets
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…
Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant…
Formalist positions towards money are considered from a perspective of formal methods in computing. The Formaleuro (FEUR) as a dimension for monetary quantities is proposed as well as the Formalbitcoin (FBTC) which represents an item ready…
Choreographic programming is a paradigm for writing coordination plans for distributed systems from a global point of view, from which correct-by-construction decentralised implementations can be generated automatically. Theory of…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the well-known construction of the real numbers using Dedekind cuts, the idea is…
We present a compositional framework for certifying resource bounds in typed programs. Terms are typed with synthesized bounds drawn from an abstract resource lattice, enabling uniform treatment of time, memory, gas, and domain-specific…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
This is a detailed and self-contained introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios as presented in Book V of…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference…