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MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems
, 2000
"... In this article we describe the data model of the MBase system, a webbased, ..."
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Cited by 46 (12 self)
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In this article we describe the data model of the MBase system, a webbased,
Planning Argumentative Texts
, 1994
"... This paper presents PROVERB, a text planner for argumentative texts. PIOVERB's main fimtm'e is that it combines global hierarchical plannillg alld illlphmncd organization of text with respect to local derivation relations in a complementary way. The Ibmmr splits the task of presenting a pa ..."
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Cited by 21 (7 self)
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This paper presents PROVERB, a text planner for argumentative texts. PIOVERB's main fimtm'e is that it combines global hierarchical plannillg alld illlphmncd organization of text with respect to local derivation relations in a complementary way. The Ibmmr splits the task of presenting a particnlar proof' subtasks of presenting suhproof. q'hc latter sinmlal.cs how the next intermediate conclnsion to be presented is chosen under the guidance of the local focus.
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 20 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...
Exploring Properties of Residue Classes
, 2000
"... We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multistrategy proof planner and two computer algebra systems. An exploration module classifies a given set and a given operation in terms of the algebraic structure they form. It th ..."
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Cited by 18 (11 self)
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We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multistrategy proof planner and two computer algebra systems. An exploration module classifies a given set and a given operation in terms of the algebraic structure they form. It then calls the proof planner to prove or refute simple properties of the operation. Moreover, we use different proof planning strategies to implement various proving techniques: from naive testing of all possible cases to elaborate techniques of equational reasoning and reduction to known cases.
Cut elimination and strong separation for substructural logics: An algebraic approach
 Annals of Pure and Applied Logic
"... Abstract. We develop a general algebraic and prooftheoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on (associative) substructural logics over the full Lambek Calculus FL (see e.g. [36, 19, 18]). We present a Gent ..."
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Cited by 4 (2 self)
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Abstract. We develop a general algebraic and prooftheoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on (associative) substructural logics over the full Lambek Calculus FL (see e.g. [36, 19, 18]). We present a Gentzenstyle sequent system GL that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a nonassociative formulation of FL. Moreover, we introduce an equivalent Hilbertstyle system HL and show that the logic associated with GL and HL is algebraizable, with the variety of residuated latticeordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of GL and various extensions, the strong separation of HL, and the finite generation of the variety of residuated latticeordered groupoids with unit. 1.
Hilbert’s “Verunglückter Beweis,” the first epsilon theorem and consistency proofs. History and Philosophy of Logic
"... Abstract. On the face of it, Hilbert’s Program was concerned with proving consistency of mathematical systems in a finitary way. This was to be accomplished by showing that that these systems are conservative over finitistically interpretable and obviously sound quantifierfree subsystems. One propo ..."
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Cited by 3 (2 self)
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Abstract. On the face of it, Hilbert’s Program was concerned with proving consistency of mathematical systems in a finitary way. This was to be accomplished by showing that that these systems are conservative over finitistically interpretable and obviously sound quantifierfree subsystems. One proposed method of giving such proofs is Hilbert’s epsilonsubstitution method. There was, however, a second approach which was not refelected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert’s first epsilon theorem and a certain “general consistency result. ” An analysis of this socalled “failed proof ” lends further support to an interpretation of Hilbert according to which he was expressly concerned with conservatitvity proofs, even though his publications only mention consistency as the main question. §1. Introduction. The aim of Hilbert’s program for consistency proofs in the 1920s is well known: to formalize mathematics, and to give finitistic consistency proofs of these systems and thus to put mathematics on a “secure foundation.” What is perhaps less well known is exactly how Hilbert thought this should be carried out. Over ten years before Gentzen developed sequent calculus formalizations
Proof Planning: A Fresh Start?
 In Proc. of the IJCAR 2001 Workshop: Future Directions in Automated Reasoning
, 2001
"... Proof Planning is a technique for automated (and interactive) theorem proving that searches for proof plans at the level of abstract methods. Proof methods consist of a chunk of mathematically motivated, recurring patterns of calculus level inferences with additional pre and postconditions tha ..."
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Cited by 2 (2 self)
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Proof Planning is a technique for automated (and interactive) theorem proving that searches for proof plans at the level of abstract methods. Proof methods consist of a chunk of mathematically motivated, recurring patterns of calculus level inferences with additional pre and postconditions that model their applicability conditions.
An essay on msicsystems
"... Abstract. A theory of manysorted implicative conceptual systems (abbreviated msicsystems) is outlined. Examples of msicsystems include legal systems, normative systems, systems of rules and instructions, and systems expressing policies and various kinds of scienti…c theories. In computer science, ..."
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Abstract. A theory of manysorted implicative conceptual systems (abbreviated msicsystems) is outlined. Examples of msicsystems include legal systems, normative systems, systems of rules and instructions, and systems expressing policies and various kinds of scienti…c theories. In computer science, msicsystems can be used in, for instance, legal information systems, decision support systems, and multiagent systems. In this essay, msicsystems are approached from a logical and algebraic perspective aiming at clarifying their structure and developing e¤ective methods for representing them. Of special interest are the most narrow links or joinings between di¤erent strata in a system, that is between subsystems of di¤erent sorts of concepts, and the intermediate concepts intervening between such strata. Special emphasis is put on normative systems, and the role that intermediate concepts play in such systems, with an eye on knowledge representation issues. In this essay, normative concepts are constructed out of descriptive concepts using operators architecture for a normregulated multiagent system is suggested, containing a scheme for how normative positions will restrict the set of actions that the agents are permitted to choose from.
British Library Cataloguing in Publication Data
"... A catalogue record for this book is available from the British Library ..."
Jaroslav Peregrin What is the Logic of Inference?
"... Abstract. The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the prooftheoretical prominency of intuitionistic logic, the forthcoming answer is that it is this ..."
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Abstract. The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the prooftheoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently singleconclusion and complying with the Gentzenian structural rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of ‘inferentially native’ logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered.