Using PVS for Interval Temporal Logic proofs, part 1: The syntactic and semantic encoding

Interval temporal logic (ITL) is a logic that is used to specify and reason about systems. The logic has a powerful proof system but rather than doing proofs by hand, which is tedious and error prone, we want a tool that can check each proof step. Instead of developing a new tool we will use the existing prototype verification system (PVS) as a basic tool. The specification language of PVS is used to encode interval temporal logic semantically and syntactically. With this we can encode the ITL proof system within PVS. Several examples of proofs in ITL that are done per hand are checked with PVS.Funded by EPSRC Research Grant GR/K2592

Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems

The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect to real-time semantics. The proposed systems subsume probabilistic real-time DC as known from the literature. A correspondence between the proposed systems and a system of probabilistic interval temporal logic with finite intervals and expanding modalities is established too.Comment: 43 page

Extracting proofs from documents

Often, theorem checkers like PVS are used to check an existing proof, which is part of some document. Since there is a large difference between the notations used in the documents and the notations used in the theorem checkers, it is usually a laborious task to convert an existing proof into a format which can be checked by a machine. In the system that we propose, the author is assisted in the process of converting an existing proof into the PVS language and having it checked by PVS. 1 Introduction The now-classic ALGOL 60 report [5] recognized three different levels of language: a reference language, a publication language and several hardware representations, whereby the publication language was intended to admit variations on the reference language and was to be used for stating and communicating processes. The importance of publication language ---often referred to nowadays as "pseudo-code"--- is difficult to exaggerate since a publication language is the most effective way..