Related papers: Analyzing Individual Proofs as the Basis of Intero…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to…
We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…
Business collaboration networks provide collaborative organizations a favorable context for automated business process interoperability. This paper aims to present a novel approach for assessing interoperability of process driven services…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…
This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
A new workflow for software development (proof-driven development) is presented. An extension of test-driven development, the new workflow utilizes the paradigm of dependently typed programming. The differences in design, complexity and…
Statistical methods are based on model assumptions, and it is statistical folklore that a method's model assumptions should be checked before applying it. This can be formally done by running one or more misspecification tests of model…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
Every theory of information, including classical and quantum, can be studied in the framework of operational probabilistic theories--where the notion of test generalizes that of quantum instrument, namely a collection of quantum operations…
Many concurrent and distributed systems are safety-critical and therefore have to provide a high degree of assurance. Important properties of such systems are frequently proved on the specification level, but implementations typically…
It is known that there exist multi-prover interactive protocols ($\mathsf{MIP}$ protocols) for the complexity class $\mathsf{NEXP}$, succinct $\mathsf{MIP}$ protocols for $\mathsf{NP}$ and multi-prover interactive protocols with shared…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.