Related papers: Refinement by interpretation in {\pi}-institutions
It has been observed that linearizability, the prevalent consistency condition for implementing concurrent objects, does not preserve some probability distributions. A stronger condition, called strong linearizability has been proposed, but…
Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to…
This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
We present a refinement of the Calculus of Inductive Constructions in which one can easily define a notion of relational parametricity. It provides a new way to automate proofs in an interactive theorem prover like Coq.
In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with…
With this positional paper we present a representation learning view on predicate invention. The intention of this proposal is to bridge the relational and deep learning communities on the problem of predicate invention. We propose a theory…
Model-driven design of software for safety-critical applications often relies on mathematically grounded techniques such as the B method. Such techniques consist in the successive applications of refinements to derive a concrete…
This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of…
A short essay presenting the State-Effect Interpretation of natural deduction rules as an explanatory framework for recent developments in proof-theoretic semantics.
We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…
Background: Understanding the distinction between function and role is vexing and difficult. While it appears to be useful, in practice this distinction is hard to apply, particularly within biology. Results: I take an evolutionary…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…
Inner interpretability is a promising field aiming to uncover the internal mechanisms of AI systems through scalable, automated methods. While significant research has been conducted on large language models, limited attention has been paid…
The challenge of creating interpretable models has been taken up by two main research communities: ML researchers primarily focused on lower-level explainability methods that suit the needs of engineers, and HCI researchers who have more…
In this paper, we give two proofs of the wellfoundedness of recursive notation systems for $\Pi_N$-reflecting ordinals. One is based on $\Pi_{N-1}^0$-inductive definitions, and the other is based on distinguished classes.
We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are…