Related papers: A heuristic prover for real inequalities
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions,…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
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…
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…
Existing reasoning evaluation paradigms suffer from different limitations: fixed benchmarks are increasingly saturated and vulnerable to contamination, while preference-based evaluations rely on subjective judgments. We argue that a core…
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
We propose a general framework for interactively learning models, such as (binary or non-binary) classifiers, orderings/rankings of items, or clusterings of data points. Our framework is based on a generalization of Angluin's equivalence…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
We introduce a systematic approach for analyzing device-independent single-prover interactive protocols under computational assumptions. This is done by establishing an explicit correspondence with Bell inequalities and nonlocal games and…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
We consider the problem of whether a given decision model, working with structured data, has individual fairness. Following the work of Dwork, a model is individually biased (or unfair) if there is a pair of valid inputs which are close to…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with…