In this paper we present a formalization of the simply typed lambda calculus with constants and with typing à la Church. It has been accomplished using the theorem prover Coq. The formalization includes, among other results, definitions of typed terms over arbitrary many-sorted signature, a substitution operating on typing judgements, an equivalence relation generalizing the concept of α-conver...

This article presents a formalization of parts of the Unified Modeling Language (UML) w.r.t. the domain of modeling time-dependant manufacturing systems. The formalization approach is based upon a set of identified general formalization steps. We investigate the applicability of UML class diagrams, Statecharts, and UML’s textual Object Constraint Language (OCL) to model manufacturing systems an...

The modal description logic AEA:/C both constitutes a promising framework for reasoning about actions and allows for the formalization of several non-first-order aspects of KR systems based on DLs. However, other nonmonotonic features of DL-based KR systems, in particular role and concept closure inside the knowledge base, lack an intuitive formalization in this modal framework. To overcome the...

We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional single-agent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search tree called increasing cost tree (ICT) and a corresponding search algorithm that finds optimal s...

The modal description logic ALCK both constitutes a promising framework for reasoning about actions and allows for the formalization of several non-rst-order aspects of KR systems based on DLs. However, other non-monotonic features of DL-based KR systems, in particular role and concept closure inside the knowledge base, lack an intuitive formalization in this modal framework. To overcome these ...

We propose a dependently typed formalization for a simple class of sequential decision problems. For this class of problems, we implement a generic version of Bellman’s backwards induction algorithm [2] and a machine checkable proof that the proposed implementation is correct. The formalization is generic. It is presented in Idris, but it can be easily translated to other dependently-typed prog...

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this article, we extend our recent mathematical formalization of this framework by providing quantitative mathematical definitions for measuring relations between concep...

The subject of research in this paper is RM-ODP, an ISO/ITU-T international standard. We investigate an important challenge that the standard faces, specifically the absence of a satisfactory formalization of its proposed conceptual framework. We report on the definition and implementation of a concrete resolution for this challenge: a single consistent formalization of the RM-ODP conceptual fr...

We report on the formalization in Ssreflect/Coq of a number of concepts and results from algorithmic game theory, including potential games, smooth games, solution concepts such as Pure and Mixed Nash Equilibria, Coarse Correlated Equilibria, -approximate equilibria, and behavioral models of games such as better-response dynamics. We apply the formalization to prove Price of Stability bounds fo...

Moessner’s Theorem describes a construction of the sequence of powers (1, 2, 3, . . . ), by repeatedly dropping and summing elements from the sequence of positive natural numbers. The theorem was presented by Moessner in 1951 without a proof and later proved and generalized in several directions. More recently, a coinductive proof of the original theorem was given by Niqui and Rutten. We presen...