2,409 research outputs found
A semantic approach to interpolation
Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially
generalize known interpolation results; all the others are new. We also discuss someapplications of our results to the theory of institutions and of algebraic specifications,and a Craig-Robinson version of these results
A semantic approach to interpolation
Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially
generalize known interpolation results; all the others are new. We also discuss someapplications of our results to the theory of institutions and of algebraic specifications,and a Craig-Robinson version of these results
Interpolation Is (Not Always) Easy to Spoil
We study a version of the Craig interpolation theorem as formulated in the framework of the theory of institutions. This formulation proved crucial in the development of a number of key results concerning foundations of software specification and formal development. We investigate preservation of interpolation under extensions of institutions by new models and sentences. We point out that some interpolation properties remain stable under such extensions, even if quite arbitrary new models or sentences are permitted. We give complete characterisations of such situations for institution extensions by new models, by new sentences, as well as by new models and sentences, respectively
The foundational legacy of ASL
Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.
The Craig Interpolation Property in First-order G\"odel Logic
In this article, a model-theoretic approach is proposed to prove that the
first-order G\"odel logic, , as well as its extension
associated with first-order relational languages enjoy the
Craig interpolation property. These results partially provide an affirmative
answer to a question posed in [Aguilera, Baaz, 2017, Ten problems in G\"odel
logic]
Matching Code and Law: Achieving Algorithmic Fairness with Optimal Transport
Increasingly, discrimination by algorithms is perceived as a societal and
legal problem. As a response, a number of criteria for implementing algorithmic
fairness in machine learning have been developed in the literature. This paper
proposes the Continuous Fairness Algorithm (CFA) which enables a
continuous interpolation between different fairness definitions. More
specifically, we make three main contributions to the existing literature.
First, our approach allows the decision maker to continuously vary between
specific concepts of individual and group fairness. As a consequence, the
algorithm enables the decision maker to adopt intermediate ``worldviews'' on
the degree of discrimination encoded in algorithmic processes, adding nuance to
the extreme cases of ``we're all equal'' (WAE) and ``what you see is what you
get'' (WYSIWYG) proposed so far in the literature. Second, we use optimal
transport theory, and specifically the concept of the barycenter, to maximize
decision maker utility under the chosen fairness constraints. Third, the
algorithm is able to handle cases of intersectionality, i.e., of
multi-dimensional discrimination of certain groups on grounds of several
criteria. We discuss three main examples (credit applications; college
admissions; insurance contracts) and map out the legal and policy implications
of our approach. The explicit formalization of the trade-off between individual
and group fairness allows this post-processing approach to be tailored to
different situational contexts in which one or the other fairness criterion may
take precedence. Finally, we evaluate our model experimentally.Comment: Vastly extended new version, now including computational experiment
Robinson consistency in many-sorted hybrid first-order logics
In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem
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