F. Giunchiglia, P. Pecchiari and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. In K.U. Shultz and F.Baader (Eds.), Frontiers of Combining Systems, Proceedings of FroCoS '96, Kluwer Series on Applied Logic, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....it is desirable not to have to build a solver from scratch if a constraint solver is already available for each component domain. Ideally, we would like to build more complex solvers by combining simpler ones, much the same way we build conventional programs by combining smaller modules (see [GPT96] for a generalized approach) In recent years, considerable research has focused on both domain and solver combinations (see, for instance, BS95a, BS95b, KS96, NO79, Sho84] although most of the efforts have been concentrated on unification problems and equational theories ( BS92, Bou93, DKR94, ....

Fausto Giunchiglia, Paolo Pecchiari, and Carolyn Talcott. Reasoning theories---towards an architecture for open mechanized reasoning systems. In F. Baader and K. U. Schulz, editors, Frontiers of Combining Systems: Proceedings of the 1st International Workshop, Applied Logic, pages 157--174, Norwell, MA, March 1996. Kluwer.

....example of such a combination is the Theorema experimental user prover PLOtter, which combines Otter and the predicate logic prover of Theorema. 5 Related Work and Conclusion The problem of integrating software reasoning systems has been studied intensively in the recent years (e.g. 2] 3] [10], 11] 13] 14] There are several platforms which try to provide a general solution to the problem ( 1] 8] 9] The interface described in this paper is not an attempt to provide such a general solution. We tried to make an interface which is simple, easy to implement, maintain and use ....

Giunchiglia, F., Pecchiari, P. and Talcott, C. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. In: F. Baader and K.U. Schulz (eds.), Frontiers of Combining Systems, Kluwer Academic Publishers (1996).

....tell us how logic functors behave: total partial, consistent complete, and reduced unreduced. This concern is complementary to the concern of actually implementing customized logics, e.g. in logical frameworks like Isabelle [Pau94] Edinburgh LF [HHP93] or Open Mechanized Reasoning Systems [GPT96] or even using a programming language. These frameworks allow users to implement a customized logic, but do not help users in proving the completeness and consistency of the resulting theorem prover. Note that one must not be left with the impression that these frameworks do not help at all. For ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories - towards an architecture for open mechanized reasoning systems. In F. Baader and K. U. Schulz, editors, 1st Int. Workshop: Frontiers of Combining Systems, pages 157--174. Kluwer Academic Publishers, March 1996.

....aspects of integration or combining systems, and the PROSPER Toolkit has no special mechanisms for ensuring the soundness of translations between the logical data of different tools. Of course this is important, but it was not emphasized in the project because other work, such as the OMRS project [29], was developing systematic frameworks for treating soundness. The remainder of this abstract gives a sketch of the technical approach taken in PROSPER and a brief account of some of the general lessons learned. Of course, other researchers have had similar ideas. There is a growing research ....

....well as rapid prototyping of combinations of tools. ETI has its own scripting and communication language, HLL, which acts much like PROSPER s combination of ML and the PII. OMRS aims to develop an open architecture for integration of reasoning systems. The architecture covers three aspects: logic [29], control strategies [17] and interaction mechanisms [6] LBA, the Logic Broker Architecture [7, 8] is a CORBA based infrastructure for the integration of reasoning systems. It provides location transparency, fowarding of requests to reasoning components via a registration subscription ....

F. Giunchiglia, P. Pecchiari, and C. Talcott, `Reasoning theories: Towards an architecture for open mechanized reasoning systems', in Frontiers of Combining Systems: First International Workshop, Munich, March 1996, edited by F. Baader and K. U. Schulz, Applied Logic Series, vol. 3 (Kluwer Academic Publishers, 1996), pp. 157--174.

....simply tell us how functors behave: total partial, consistent complete, and reduced unreduced. This concern is complemantary to the concern of actually implementing customized logics, e.g. in logical frameworks like Isabelle [Pau94] Edinburgh 111 LF [HHP93] or Open Mechanized Reasoning Systems [GPT96]. These frameworks allow users to implement a customized logic, but do not help users in proving the completeness of the resulting theorem prover. In essence, this work is more similar to works on static program analysis toolbox (e.g. PAG [AM95] where authors assemble known results to combine ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories - towards an architecture for open mechanized reasoning systems. In F. Baader and K. U. Schulz, editors, 1st Int. Workshop: Frontiers of Combining Systems, pages 157-174. Kluwer Academic Publishers, March 1996.

....Another is using one system to check another. There is also an ecumenical interest in forging links between theorem proving communities. There has been some work in providing a general framework for different logics. The MathWeb [AHJ 00] and Open Mechanized Reasoning Systems projects [GPT94] aim to provide such a framework. However, it seems there is still much to do at the level of getting individual proof assistants, with their different logics, to understand each other. In this article we will examine the specific case of translating HOL [GM93] proofs to a Coq [BBC 97] ....

Fausto Giunchiglia, Paolo Pecchiari, and Carolyn Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. Technical Note CS-TN-94-15, Stanford University, Department of Computer Science, December 1994.

....level, the computations carried out by the system amount to constructing and manipulating structures consisting of assertions connected through elementary deduction steps (like proof trees) The key concept of the logic layer is that of reasoning theory. Roughly speaking, a reasoning theory (RTh) [16] consists of a set of sequents (i.e. assertions) and a set of inference rules over such sequents. An RTh de nes a set of reasoning structures, i.e. graphs labeled by sequents and rules. The notion of reasoning structure generalizes the standard concept of derivation so as to capture, e.g. ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Technical Report 9409-15, IRST, Trento, Italy, 1994.

....Their solutions do heavily depend on the integrated systems. The question how different theorem provers can be easily combined in a single environment that is flexible enough to handle both replacement and addition of systems has led to the concept of Open Mechanized Reasoning Systems [ Giunchiglia et al. 1996 ] Within an OMRS, theorem provers can be viewed as easily replaceable plug and play components. The concept of OMRS has been generalised to Open Mathematical Environments [ Homann and Calmet, 1995 ] where all kinds of mathematical services [ Homann and Calmet, 1996 ] can be combined. It turned ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories -- Towards an Architecture for Open Mechanized Reasoning Systems. In F. Baader and K. Schulz, editors, Frontiers of combining systems, volume 3 of Applied logic series, pp. 157--174. Kluwer Academic Publishers, Dordrecht, 1996.

....theorem proving suffers from. Meta level control knowledge is a means to restrict the search space. In CL A M , for instance, the preconditions of methods carry this information. Another option for representing control knowledge declaratively is to separate it in control rules, as proposed in [5, 6]. These two attempts aim at a modular and principled way to handle uninstantiated control information. An example of a control rule in [5] is induction hypothesis applicable then next method(fertilize) Whereas control knowledge that restricts the search is usually uninstantiated and exists ....

....and the current partial proof. Thus, the description can be quite powerful. Control rules can also capture knowledge about (hierarchical) proof patterns for a class of proofs. As stated above, first attempts to use separate control rules in theorem proving are on their way. The framework in [6], however, tries to use a uniform representation of logic, control, and mixed logic control rules. The emphasize is on passing the explicit control knowledge from step to step. 5 Conclusion We emphasized the two requirements for the representation of proofs, 1) the explicit representation and ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Technical Report 9409-15, IRST, Trento, Italy, 1994.

....application of rules, tactics and external reasoners cannot be automated. As an environment that is especially designed to support the combination of interactive and automated theorem proving together with the use of already existing reasoning systems, is the Open Mechanized Reasoning System [12, 11] that has been extended to facilitate computer algebra systems [6] While the concept of a reasoning structure to represent explicit proof states is similar to our concept of a proof object, external reasoners are connected as plug and play components which requires signi cant 14 changes to their ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories - Towards an Architecture for Open Mechanized Reasoning Systems. In Proc. of Frontiers of Combining Systems, pages 157-174, 1996.

....and more generally for reasoning about components of open distributed systems. Interaction semantics is endowed with an algebra structure that provides a basis for modular reasoning about construction and transformation of components specified as abstract actor systems [188] The OMRS project [55, 53] is a joint project with the Mechanized Reasoning Group of IRST in Trento, Italy. The ultimate goal of this work is to provide a framework and a methodology for constructing and modifying complex reasoning systems by composing and integrating simpler modules. The OMRS framework has been used to ....

F. Giunchiglia, P. Pecchiari, and C. L. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. Technical Report 9409-15, IRST, November 1994. Also appears as Stanford University Computer Science Department Technical Note STAN-CS-94-TN-15.

....constructing and interoperating reasoning and other tools is related to the many existing proof systems that are in fact a composition of multiple reasoning modules and to the numerous experiments in augmenting and combining existing proof systems. A detailed survey and discussion can be found in [54]. We give here a brief summary. The Boyer Moore prover NQTHM [14, 16] and the more recent ACL2 [82] combines techniques for propositional reasoning, equality reasoning, typeset inference, term rewriting, and linear arithmetic. RRL [80, 81] includes a completion procedure, rewriting, ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems, 1996. submitted for publication.

....modules are reified as data, it is possible and easy to write programs that manipulate, transform, and adapt other programs, including adaptation of software modules at runtime that may depend on changes in their environment. Open Mechanized Reasoning Systems Open Mechanized Reasoning Systems [53] is a general framework for modular construction and interoperation of mechanized reasoning systems. The ultimate goal of this work is to provide a framework and a methodology in which users, as well as system developers, can construct complex reasoning systems by composing existing modules, or ....

....and more generally for reasoning about components of open distributed systems. Interaction semantics is endowed with an algebra structure that provides a basis for modular reasoning about construction and transformation of components specified as abstract actor systems [188] The OMRS project [55, 53] is a joint project with the Mechanized Reasoning Group of IRST in Trento, Italy. The ultimate goal of this work is to provide a framework and a methodology for constructing and modifying complex reasoning systems by composing and integrating simpler modules. The OMRS framework has been used to ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. In Workshop on Frontiers of Combining Systems FROCOS'96, 1996.

No context found.

Giunchiglia, F., Pecchiari, P., and Talcott, C. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Tech. Rep. 9409-15, IRST, Trento, Italy, 1994. Short version in Proc. of the First International Workshop on Frontiers of Combining Systems (FroCoS'96), Munich, Germany, 1996.

....mechanized reasoning systems such as, e.g. Theorem Provers and Computer Algebra Systems. Our approach to the problem is to provide a framework for specifying mechanized reasoning systems and to use speci cations as a starting point for integration. We build on top of the work presented in [9] which introduces the notion of Open Mechanized Reasoning Systems (OMRS) as a speci cation framework for integrating reasoning systems. An OMRS speci cation consists of three components: the logic component, the control component, and the interaction component. In this paper we focus on the ....

....can be very dicult to achieve. A set of representative experiences showing the viability of the approach is described in [1,13,14,2] In both cases the main source of diculty is the complexity of the services provided by state of the art implementations. We build on top of the work presented in [9] which introduces the notion of Open Mechanized Reasoning Systems (OMRS) as a speci cation framework for extending or integrating reasoning systems. An OMRS speci cation consists of three components: the logic component (specifying the assertions manipulated by the system and the elementary ....

[Article contains additional citation context not shown here]

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Technical Report 940915, IRST, Trento, Italy,

....symbolic mathematical service should be structurally organized as an open architecture able to provide services like, e.g. proving that a formula is a theorem, or computing a definite symbolic integral, and to be able, if and when necessary, to rely on similar services provided by other tools. In [9], the Open Mechanized Reasoning System (OMRS) architecture was introduced as a mean to specify and implement reasoning systems (e.g. theorem provers) as logical services. In [6] this approach has been recasted to symbolic computer algebra systems. In this paper, we show a generalization of this ....

.... [ is the operation for application of instantiations to objects and to constraints, that is [ O Theta I O ] and [ C Theta I C ] In order to qualify as a system of symbolic entities, Esys , and more specifically j= I , and [ must meet certain requirements, which can be lifted from [9]. The basic operations which can be performed over a system of symbolic entities are defined in a set theoretic way, as relations between single entities and tuples of entities, instantiations and constraints. These relations are required to be closed w.r.t. instantiation. Namely, let Esys = O ; ....

[Article contains additional citation context not shown here]

Giunchiglia, F., Pecchiari, P., and Talcott, C. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Tech. Rep. 940915, IRST, Trento, Italy,

....it can participate in what questions it might ask or answer, when, and what the answers mean. Starting with this in mind, we structure an OMRS in three layers: the underlying deductive machinery; strategies for controlling inference; and interaction capabilities. We refer the reader to [11,12,8] for further discussion of the motivation for and applications of OMRS. The underlying deduction machinery of an OMRS is described by a reasoning theory . The idea of reasoning theory has its roots in the notion of reasoning structure. Reasoning structures were invented as part of a project to ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems, 1998. submitted for publication.

....structure corresponds to the proof term model of rewriting logic. The objective of this paper is to make this correspondence more precise, and to indicate how the correspondence might be used in different ways to enrich both the OMRS world and the rewriting logic world. 1 Introduction In [11] the notion of an Open Mechanized Reasoning System (OMRS) was introduced. The long term objective of the OMRS project is to provide a framework for specifying and structuring reasoning systems, and a technology for integrating and interoperating diverse proof systems with each other 1 Research ....

....it can participate in what questions it might ask or answer, when, and what the answers mean. Starting with this in mind, we structure an OMRS in three layers: the underlying deductive machinery; strategies for controlling inference; and interaction capabilities. We refer the reader to [11,12,8] for further discussion of the motivation for and applications of OMRS. The underlying deduction machinery of an OMRS is described by a reasoning theory . The idea of reasoning theory has its roots in the notion of reasoning structure. Reasoning structures were invented as part of a project to ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. In Workshop on Frontiers of Combining Systems FROCOS'96, 1996.

....and composition to consider also annotations. As an example, we give a modular specification of the top level control (known as waterfall) of NQTHM, the Boyer Moore theorem prover. 1 Introduction Reasoning theories are the core of the OMRS (Open Mechanized Reasoning System(s) framework [14] for the specification of complex, heterogeneous reasoning systems. The long term goal of OMRS is to provide a technology which will allow the development, integration and interoperation of theorem provers (and similar systems, e.g. computer algebra systems and model checkers) in a principled ....

....instantiating inference rules and linking them by matching premisses to conclusions. We write ds : f cng sq ) sq 0 to indicate that ds is a derivation structure with conclusions the list of sequents sq 0 , premisses the list sq , and side conditions the list of constraints cn. See [14] for a detailed description of reasoning theories. 2.1 Sequent signatures and ERThs In this paper we focus on equationally presented reasoning theories (ERThs) An ERTh consists of a sequent signature and a labelled set of rules of inference. A sequent signature consists of an equational ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. In Workshop on Frontiers of Combining Systems FROCOS'96, 1996.

.... conjecture being proved) control information (e.g. some user supplied hints used by the prover to select among many possible inference steps) and interaction information used for the interface (e.g. formatting information for messages to be printed on the screen) In the OMRS architecture [19], these aspects are clearly separated into three layered components, as shown in the right part of Figure 1. Thus, we can state the following equation: OMRS = Logic Control Interaction The OMRS components are inherently related in a hierarchical way: the definition of the logic is ....

....conditions of inference rules (e.g. that a variable does not occur free in a formula) This raises the need for an explicit representation of (possibly schematic) constraints, as well as for a mechanism to check constraint satisfaction. In order to conveniently formally model the above aspects, [19] introduces the following notion of sequent system: Ssys = S ; C ; j= I ; S is the set of sequents. C is the set of constraints, and j= P (C ) C ) is a satisfaction relation on constraints 3 . I is the set of instantiation maps (or just instantiations) and [ is the operation ....

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F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Technical Report 940915, IRST, Trento, Italy,

....component of the simplification process of NQTHM, the Boyer Moore theorem prover. 1. Introduction Our ultimate goal is to provide a framework and a methodology which will allow users to construct and extend complex reasoning systems by composing existing modules in a plug and play manner. In [7] a general architecture is proposed for a class of reasoning modules and systems called Open Mechanized Reasoning Systems (OMRSs) An OMRS has three components: a logic component which consists of the assertions manipulated by the OMRS and the elementary deductions upon them; a control component ....

....strategies of the OMRS; an interaction component which provides the OMRS with the capability of interacting with other systems, including OMRSs and human users. That work is focused on the development of the theory underlying the logic component. This paper follows on the work described in [7]. Here we show how the theory and methodology introduced in [7] can be used in practice to specify the logic component of the simplification process of the Boyer Moore theorem prover, NQTHM [5, 4] We stress that the choice of NQTHM is not by chance. First of all a better understanding of the ....

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F. Giunchiglia, P. Pecchiari, and C. L. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. Technical Report 9409-15, IRST, November

....in principle the prover itself could be questioned. Several approaches to this problem are under development. Some of these aim at the development of logging checking mechanisms for full blown provers (e.g. 6] Others aim at the development of a provably correct prover, see for instance [2] and [3]. Finally, the certification provided by the Verifier depends on the correct implementation and execution of the Checker. The confidence in this assumption is rather high, as the Checker has been designed to be validated by end users, and given its simplicity also the compilation and the ....

F. Giunchiglia, P. Pecchiari, and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Technical Report 9409-15, IRST, Trento, Italy, 1994.

No context found.

F. Giunchiglia, P. Pecchiari and C. Talcott. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. In K.U. Shultz and F.Baader (Eds.), Frontiers of Combining Systems, Proceedings of FroCoS '96, Kluwer Series on Applied Logic, 1996.

No context found.

F. Giunchiglia, P. Pecchiari, and C. L. Talcott. Reasoning theories: Towards an architecture for open mechanized reasoning systems. Technical Report 9409-15, IRST, November

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