Trustworthy Formal Natural Language Specifications

Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may have been mistranslated from a claim made in natural language. This is especially problematic when using proof assistants to formally verify the correctness of software with respect to a natural language specification. The translation from informal to formal remains a challenging, time-consuming process that is difficult to audit for correctness. This paper shows that it is possible to build support for specifications written in expressive subsets of natural language, within existing proof assistants, consistent with the principles used to establish trust and auditability in proof assistants themselves. We implement a means to provide specifications in a modularly extensible formal subset of English, and have them automatically translated into formal claims, entirely within the Lean proof assistant. Our approach is extensible (placing no permanent restrictions on grammatical structure), modular (allowing information about new words to be distributed alongside libraries), and produces proof certificates explaining how each word was interpreted and how the sentence's structure was used to compute the meaning. We apply our prototype to the translation of various English descriptions of formal specifications from a popular textbook into Lean formalizations; all can be translated correctly with a modest lexicon with only minor modifications related to lexicon size.Comment: arXiv admin note: substantial text overlap with arXiv:2205.0781

Solving an Unsteady-state and Non-uniform Heat Conduction Transfer Problem Using Discrete-analytical Method

AbstractThe paper presents one of the methods to determine heat spread patterns in objects. Mathematical model of the process is a differential equation of the second order with initial and boundary conditions, which can be solved by only one function U(x, y, z, t). In this paper the problem of unsteady-state and non-uniform heat conduction transfer for 2 dimensions, with imposed initial and boundary conditions of the first, second and third kind, is solving using discrete-analytical method. The main idea of this method is to combine discrete and analytical method. In this case, initial problem is divided to 2 stages: in the first stage a discrete technique along ones directions will be applied; in the second stage an analytical method along other directions will be applied. The result will be a discrete set of analytical functions. For “discrete stage” is used a well-known method of finite differences, and for analytical stage is applied the virtue of the matrix exponent. In the general case, the problem can be submitted in operator form with non-orthogonal quadrangular mesh which is topologically equivalent to square mesh

An experimental study of flow over flat and axisymmetric bodies

The technique and results of an experimental study of the flow structure and critical parameters of the flow over flat and axisymmetric bodies in a range of the Mach numbers (M = 2 ÷ 5) are presented

An experimental study of flow over flat and axisymmetric bodies

The technique and results of an experimental study of the flow structure and critical parameters of the flow over flat and axisymmetric bodies in a range of the Mach numbers (M = 2 ÷ 5) are presented

Building Helpful Virtual Agents Using Plan Recognition and Planning

This paper presents a new model of cooperative behavior based on the interaction of plan recognition and automated planning.  Based on observations of the actions of an "initiator" agent, a  "supporter" agent uses plan recognition to hypothesize the plans  and goals of the initiator.  The supporter agent then proposes and  plans for a set of subgoals it will achieve to help the initiator.  The approach is demonstrated in an open-source, virtual robot  platform

An experimental study of flow over flat and axisymmetric bodies

The technique and results of an experimental study of the flow structure and critical parameters of the flow over flat and axisymmetric bodies in a range of the Mach numbers (M = 2 ÷ 5) are presented