4,882 research outputs found
Advanced Proof Viewing in ProofTool
Sequent calculus is widely used for formalizing proofs. However, due to the
proliferation of data, understanding the proofs of even simple mathematical
arguments soon becomes impossible. Graphical user interfaces help in this
matter, but since they normally utilize Gentzen's original notation, some of
the problems persist. In this paper, we introduce a number of criteria for
proof visualization which we have found out to be crucial for analyzing proofs.
We then evaluate recent developments in tree visualization with regard to these
criteria and propose the Sunburst Tree layout as a complement to the
traditional tree structure. This layout constructs inferences as concentric
circle arcs around the root inference, allowing the user to focus on the
proof's structural content. Finally, we describe its integration into ProofTool
and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785
TLA+ Proofs
TLA+ is a specification language based on standard set theory and temporal
logic that has constructs for hierarchical proofs. We describe how to write
TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's
mutual exclusion algorithm as a simple example to describe the features of
TLAPS and show how it and the Toolbox (an IDE for TLA+) help users to manage
large, complex proofs.Comment: A shorter version of this article appeared in the proceedings of the
conference Formal Methods 2012 (FM 2012, Paris, France, Springer LNCS 7436,
pp. 147-154
Category Theory for Autonomous Robots: The Marathon 2 Use Case
Model-based systems engineering (MBSE) is a methodology that exploits system
representation during the entire system life-cycle. The use of formal models
has gained momentum in robotics engineering over the past few years. Models
play a crucial role in robot design; they serve as the basis for achieving
holistic properties, such as functional reliability or adaptive resilience, and
facilitate the automated production of modules. We propose the use of formal
conceptualizations beyond the engineering phase, providing accurate models that
can be leveraged at runtime. This paper explores the use of Category Theory, a
mathematical framework for describing abstractions, as a formal language to
produce such robot models. To showcase its practical application, we present a
concrete example based on the Marathon 2 experiment. Here, we illustrate the
potential of formalizing systems -- including their recovery mechanisms --
which allows engineers to design more trustworthy autonomous robots. This, in
turn, enhances their dependability and performance
Knowledge in Artificial Intelligence Systems: Searching the Strategies for Application
The studies based on auto-epistemic logic are pointed out as an advanced direction for development of artificial intelligence (AI). Artificial intelligence is taken as a system that imitates the solution of complicated problems by human during the course of life. The structure of symbols and operations, by which intellectual solution is performed, as well as searching the strategic reference points for those solutions, which are caused by certain structures of symbols and operations, – are considered among the main issues in analysis of AI and its applications. Expert systems are interpreted as a kind of intelligent systems; different ways to represent knowledge (such as logical model, frame-based and production systems, semantic networks) are described within the framework of cognitive studies of AI. The presentation of knowledge is stated to be the methodology for modeling and formalization of conceptual knowledge in the field of engineering
A Computational Approach to Reflective Meta-Reasoning about Languages with Bindings
We present a foundation for a computational meta-theory of languages with bindings implemented in a computer-aided formal reasoning environment. Our theory provides the ability to reason abstractly about operators, languages, open-ended languages, classes of languages, etc. The theory is based on the ideas of higher-order abstract syntax, with an appropriate induction principle parameterized over the language (i.e. a set of operators) being used. In our approach, both the bound and free variables are treated uniformly and this uniform treatment extends naturally to variable-length bindings. The implementation is reflective, namely there is a natural mapping between the meta-language of the theorem-prover and the object language of our theory. The object language substitution operation is mapped to the meta-language substitution and does not need to be defined recursively. Our approach does not require designing a custom type theory; in this paper we describe the implementation of this foundational theory within a general-purpose type theory. This work is fully implemented in the MetaPRL theorem prover, using the pre-existing NuPRL-like Martin-Lof-style computational type theory. Based on this implementation, we lay out an outline for a framework for programming language experimentation and exploration as well as a general reflective reasoning framework. This paper also includes a short survey of the existing approaches to syntactic reflection
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