Deduction modulo theory

This paper is a survey on Deduction modulo theor

Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo

This articles is a structured bibliography on theorem provers, approaches to theorem proving, and theorem proving applications inspired from Satchmo, the model generation theorem prover developed in the mid 80es of the 20th century at ECRC, the European Computer- Industry Research Centre. Note that the bibliography given in this article is not exhaustive

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Applying automated deduction to natural language understanding

AbstractVery few natural language understanding applications employ methods from automated deduction. This is mainly because (i) a high level of interdisciplinary knowledge is required, (ii) there is a huge gap between formal semantic theory and practical implementation, and (iii) statistical rather than symbolic approaches dominate the current trends in natural language processing. Moreover, abduction rather than deduction is generally viewed as a promising way to apply reasoning in natural language understanding. We describe three applications where we show how first-order theorem proving and finite model construction can efficiently be employed in language understanding.The first is a text understanding system building semantic representations of texts, developed in the late 1990s. Theorem provers are here used to signal inconsistent interpretations and to check whether new contributions to the discourse are informative or not. This application shows that it is feasible to use general-purpose theorem provers for first-order logic, and that it pays off to use a battery of different inference engines as in practice they complement each other in terms of performance.The second application is a spoken-dialogue interface to a mobile robot and an automated home. We use the first-order theorem prover spass for checking inconsistencies and newness of information, but the inference tasks are complemented with the finite model builder mace used in parallel to the prover. The model builder is used to check for satisfiability of the input; in addition, the produced finite and minimal models are used to determine the actions that the robot or automated house has to execute. When the semantic representation of the dialogue as well as the number of objects in the context are kept fairly small, response times are acceptable to human users.The third demonstration of successful use of first-order inference engines comes from the task of recognising entailment between two (short) texts. We run a robust parser producing semantic representations for both texts, and use the theorem prover vampire to check whether one text entails the other. For many examples it is hard to compute the appropriate background knowledge in order to produce a proof, and the model builders mace and paradox are used to estimate the likelihood of an entailment