Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning modules and systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and human users. Second, it develops the theory underlying the reasoning theory component. This development is motivated by an analysis of state of the art systems. The resulting theory is then validated by using it to describe the integration of the linear arithmetic module into the simplification process of the Boyer-Moore system, NQTHM. 1. Plug and Play Reasoning Devices-- An Impossible Dream?
|
530
|
A framework for defining logics
– Harper, Honsell, et al.
- 1993
|
|
495
|
Introduction to Metamathematics
– Kleene
- 1952
|
|
491
|
A Computational Logic
– Boyer, Moore
- 1979
|
|
399
|
Institutions: Abstract model theory for specification and programming
– Goguen, Burstall
- 1992
|
|
389
|
PVS: A prototype verification system
– Owre, Rushby, et al.
- 1992
|
|
387
|
A Computational Logic Handbook
– Boyer, Moore
- 1988
|
|
368
|
Conditional rewriting logic as a unified model of concurrency
– Meseguer
- 1992
|
|
270
|
Simplification by cooperating decision procedures
– Nelson, Oppen
- 1979
|
|
263
|
A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification
– Miller
- 1991
|
|
238
|
Symbolic Logic and Mechanical Theorem Proving
– Chang, Lee
- 1973
|
|
206
|
C.: HOL: A proof generating system for Higher-Order Logic
– Gordon
- 1988
|
|
189
|
Natural Deduction: a Proof-Theoretical Study. Almquist and Wiskell
– Prawitz
- 1965
|
|
179
|
Mathematical Logic
– Shoenfield
- 1967
|
|
161
|
Rippling: A heuristic for guiding inductive proofs
– Bundy, Stevens, et al.
- 1993
|
|
156
|
Isabelle: The next 700 theorem provers
– Paulson
- 1990
|
|
151
|
General logics
– Meseguer
- 1989
|
|
134
|
Rewriting logic as a logical and semantic framework
– Mart'i-Oliet, Meseguer
- 1996
|
|
133
|
Deciding combinations of theories
– Shostak
- 1984
|
|
115
|
Higher-order critical pairs
– Nipkow
- 1991
|
|
104
|
Integrating decision procedures into heuristic theorem provers: A case study with linear arithmetic
– Boyer, Moore
- 1988
|
|
96
|
Edinburgh LCF, a mechanical logic of computation
– Gordon, Milner, et al.
- 1977
|
|
90
|
Simple consequence relations
– Avron
- 1991
|
|
86
|
An integration of model-checking with automated proof checking
– Rajan, Shankar, et al.
- 1995
|
|
83
|
Imps: An interactive mathematical proof system
– Farmer, Guttman, et al.
- 1993
|
|
70
|
The semantics of reflected proof
– Allen, Constable, et al.
- 1990
|
|
63
|
Contextual reasoning
– Giunchiglia
- 1993
|
|
52
|
Theorems and Algorithms: an Interface between Isabelle and Maple
– Ballarin, Homann, et al.
- 1995
|
|
45
|
Jos'e Meseguer, Kokichi Futatsugi, and Jean-Pierre Jouannaud. Introducing OBJ
– Goguen, Winkler
- 1996
|
|
40
|
Logic and Computation
– Paulson
- 1987
|
|
39
|
Analytica — a theorem prover for Mathematica
– Clarke, Zhao
- 1991
|
|
37
|
Axiomatizing reflective logics and languages
– Clavel, Meseguer
- 1996
|
|
36
|
An overview of RRL (rewrite rule laboratory
– Kapur, Zhang
- 1989
|
|
35
|
Extending the HOL Theorem Prover with a Computer Algebra System to Reason about the Reals
– Harrison, Th'ery
|
|
35
|
CAS/PI: a Portable and Extensible Interface for Computer Algebra Systems
– Kajler
- 1992
|
|
32
|
Design Goals for ACL2
– Kaufmann, Moore
- 1994
|
|
32
|
A decidable fragment of predicate calculus
– Ketonen, Weyhrauch
- 1984
|
|
29
|
The GETFOL Manual - GETFOL version 1
– Giunchiglia
- 1992
|
|
26
|
Finitary inductively presented logics
– Feferman
- 1989
|
|
25
|
A theory of binding structures and applications to rewriting
– Talcott
- 1993
|
|
22
|
A Verification Condition Generator for FORTRAN
– Boyer, Moore
- 1981
|
|
17
|
Mechanizing Proof Theory: Resource-Aware Logics and ProofTransformations to Extract Implicit Information
– Bellin
- 1990
|
|
16
|
The HOL-Voss System: Model-Checking inside a General-Purpose Theorem-Prover
– Joyce, Seger
|
|
15
|
Structures for Symbolic Mathematical Reasoning and Computation
– Homann, Calmet
- 1996
|
|
14
|
Multilanguage systems
– Giunchiglia
- 1991
|
|
14
|
An overview of the Tecton proof system
– Kapur, Musser, et al.
- 1994
|
|
11
|
Structure and Representation in LF
– Harper, Sannella, et al.
- 1989
|
|
11
|
Prolegomena to a theory of formal reasoning
– Weyhrauch
- 1980
|
|
10
|
Reflection in rewriting logic
– Clavel, Meseguer
- 1996
|
|
10
|
First-order theorem proving using conditional rewrite rules
– Kapur, Zhang
- 1988
|
|
10
|
Combinatory Reduction Systems. Number 127
– Klop
- 1980
|