In this article we describe the data model of the MBase system, a webbased,

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Real-world applications of automated theorem proving require modern software environments that enable modularisation, networked inter-operability, robustness, and scalability. These requirements are met by the Agent-Oriented 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...

We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multi-strategy 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.

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 quantifier-free 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 so-called “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 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 post-conditions that model their applicability conditions.

Abstract. Modus Ponens says that if you know A and you know that A implies B, then you know B. This is a basic rule that we take for granted

Abstract. A theory of many-sorted implicative conceptual systems (abbreviated msic-systems) is outlined. Examples of msic-systems include legal systems, normative systems, systems of rules and instructions, and systems expressing policies and various kinds of scienti…c theories. In computer science, msic-systems can be used in, for instance, legal information systems, decision support systems, and multi-agent systems. In this essay, msic-systems 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 norm-regulated multi-agent system is suggested, containing a scheme for how normative positions will restrict the set of actions that the agents are permitted to choose from.