1,186 research outputs found
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
Automated Reasoning and Robotics
A most important quality in robotics is the work done in the development of automated reasoning techniques. This model of reasoning works on the assistance of computer programs and just as it is in other fields, it has worked to aid in the answering of certain open questions. The aim of this survey is to study the applications of automated reasoning in the field of robotics and to evaluate its efficiency as a reasoning technique when applied. It is based generally on research into reasoning techniques applied to robotics and running an evaluation in contrast to automated reasoning to determine the rates of effectiveness between them. This process involves a basic understanding of how reasoning is implemented in relation to robotics, after which varying reasoning techniques and applications are discussed and compared in relation to automated reasoning and how automated reasoning would work to enhance results retrieved. The primary objective in this study is to identify the effectiveness of automated reasoning techniques to other techniques available and it begins with an introduction providing an overview of the concepts discussed before proceeding to examine the technicalities involved and which level of technicality is best
Learning-Assisted Automated Reasoning with Flyspeck
The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
A Semantic Similarity Measure for Expressive Description Logics
A totally semantic measure is presented which is able to calculate a
similarity value between concept descriptions and also between concept
description and individual or between individuals expressed in an expressive
description logic. It is applicable on symbolic descriptions although it uses a
numeric approach for the calculus. Considering that Description Logics stand as
the theoretic framework for the ontological knowledge representation and
reasoning, the proposed measure can be effectively used for agglomerative and
divisional clustering task applied to the semantic web domain.Comment: 13 pages, Appeared at CILC 2005, Convegno Italiano di Logica
Computazionale also available at
http://www.disp.uniroma2.it/CILC2005/downloads/papers/15.dAmato_CILC05.pd
Efficient Data Structures for Automated Theorem Proving in Expressive Higher-Order Logics
Church's Simple Theory of Types (STT), also referred to as classical higher-order logik, is an elegant and expressive formal system built on top of the simply typed λ-calculus. Its mechanisms of explicit binding and quantification over arbitrary sets and functions allow the representation of complex mathematical concepts and formulae in a concise and unambiguous manner. Higher-order automated theorem proving (ATP) has recently made major progress and several sophisticated ATP systems for higher-order logic have been developed, including Satallax, Osabelle/HOL and LEO-II. Still, higher-order theorem proving is not as mature as its first-order counterpart, and robust implementation techniques for efficient data structures are scarce.
In this thesis, a higher-order term representation based upon the polymorphically typed λ-calculus is presented. This term representation employs spine notation, explicit substitutions and perfect term sharing for efficient term traversal, fast β-normalization and reuse of already constructed terms, respectively. An evaluation of the term representation is performed on the basis of a heterogeneous benchmark set. It shows that while the presented term data structure performs quite well in general, the normalization results indicate that a context dependent choice of reduction strategies is beneficial.
A term indexing data structure for fast term retrieval based on various low-level criteria is presented and discussed. It supports symbol-based term retrieval, indexing of terms via structural properties, and subterm indexing
- …