93,577 research outputs found
Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories
The computer-mechanization of an ambitious explicit ethical theory, Gewirth's
Principle of Generic Consistency, is used to showcase an approach for
representing and reasoning with ethical theories exhibiting complex logical
features like alethic and deontic modalities, indexicals, higher-order
quantification, among others. Harnessing the high expressive power of Church's
type theory as a meta-logic to semantically embed a combination of quantified
non-classical logics, our work pushes existing boundaries in knowledge
representation and reasoning. We demonstrate that intuitive encodings of
complex ethical theories and their automation on the computer are no longer
antipodes.Comment: 14 page
Rewriting and Well-Definedness within a Proof System
Term rewriting has a significant presence in various areas, not least in
automated theorem proving where it is used as a proof technique. Many theorem
provers employ specialised proof tactics for rewriting. This results in an
interleaving between deduction and computation (i.e., rewriting) steps. If the
logic of reasoning supports partial functions, it is necessary that rewriting
copes with potentially ill-defined terms. In this paper, we provide a basis for
integrating rewriting with a deductive proof system that deals with
well-definedness. The definitions and theorems presented in this paper are the
theoretical foundations for an extensible rewriting-based prover that has been
implemented for the set theoretical formalism Event-B.Comment: In Proceedings PAR 2010, arXiv:1012.455
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
A recovery operator for nontransitive approaches
In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities
A recovery operator for non-transitive approaches
In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities.Fil: Barrio, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; ArgentinaFil: Pailos, Federico Matias. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; ArgentinaFil: Szmuc, Damián Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; Argentin
A theorem prover-based analysis tool for object-oriented databases
We present a theorem-prover based analysis tool for object-oriented database systems with integrity constraints. Object-oriented database specifications are mapped to higher-order logic (HOL). This allows us to reason about the semantics of database operations using a mechanical theorem prover such as Isabelle or PVS. The tool can be used to verify various semantics requirements of the schema (such as transaction safety, compensation, and commutativity) to support the advanced transaction models used in workflow and cooperative work. We give an example of method safety analysis for the generic structure editing operations of a cooperative authoring system
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