MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to modal logics. The motivations of our proposal are technical, epistemological and implementational. From a technical point of view, we prove, among other things, that the set of theorems of the most common modal logics can be embedded (under the obvious bijective mapping between a modal and a first order language) into that of the corresponding ML systems. Moreover, we show that ML systems have properties not holding for modal logics and argue that these properties are justified by our intuitions. This claim is motivated by the study of how ML systems can be used in the representation of beliefs (more generally, propositional attitudes) and provability, two areas where modal logics have been extensively used. Finally, from an implementation point of view, we argue that ML systems resemble closely the current practice in the computer representation of propositional attitudes and metatheoretic theorem proving.

In this paper we propose a metatheory, MT which represents the computation which implements its object theory, OT, and, in particular, the computation which implements deduction in OT. To emphasize this fact we say that MT is a metatheory of a mechanized object theory. MT has some "unusual" properties, e.g. it explicitly represents failure in the application of inference rules, and the fact that large amounts of the code implementing OT are partial, i.e. they work only for a limited class of inputs. These properties allow us to use MT to express and prove tactics, i.e. expressions which specify how to compose possibly failing applications of inference rules, to interpret them procedurally to assert theorems in OT, to compile them into the system implementation code, and, finally, to generate MT automatically from the system code. The definition of MT is part of a larger project which aims at the implementation of self-reflective systems, i.e. systems which are able to intros...

The main premise of this paper is that certain kinds of non-monotonic reasoning can be solved within first order logic in a simple monotonic way by formulating problems in a suitable environment. Any problem is formalized as a set of contexts, where a context is a (first order) formalization of a piece of the problem. Reasoning comes out as a result of deduction in different contexts. The claim is that proofs built in this way are clearer and better resemble the kind of explanation that humans give when describing some phenomenon. This thesis is articulated discussing the example about non-monotonic reasoning reported in [MD80].

We show how explicit control strategies can be represented in a declarative (classical) metatheory as first order formulae (proof plans). Proof plans can be reasoned about (by metatheoretic theorem proving) to modify the search strategy and "executed" (by suitably "interpreting" them in terms of the deductive machinery implementation code) to prove a theorem in the object theory. The resulting architecture is uniform as it becomes possible to define a tower of metatheories, each using the same deductive machinery, each (but the lowest) being able to represent proof plans with formulae of the same shape. Plan formation at one level can be obtained by plan execution one level up. The realization of these ideas in the GETFOL system is briefly described via the implementation of a simplified version of the Boyer and Moore theorem prover. 1 Introduction The idea of using metatheories in theorem proving has been extensively studied in the past, a not exhaustive list is [DS79, Wey8...

The origins of this work go back to research on building systems for the automatic synthesis of programs from specifications, extending the capabilities of existing ones, making several systems cooperate, and integrating them into a larger programming environment. The experiences were rather frustrating. Program synthesis systems tend to be ad hoc implementations rather than being built systematically and well structured. It is not surprising that they have the same problems as other software products: there are all kinds of unexpected bugs, maintanance and modifications become increasingly difficult, and cooperation with other synthesizers is nearly impossible despite of the fact that ideas behind the synthesis strategies show many similarities if explained verbally. Apart from human shortcomings the main reason for this problem lies in a lack of formality in the steps from describing an idea on paper to its realization on a computer. Such formality, however, is difficult to achieve, extremely time consuming, and slows down the initial progress of a synthesis system. This is a price which many scientists are not willing to pay. On the other hand, the insufficiencies of current “ad hoc ” systems are hardly acceptable — and there are no exceptions — and there is a need for tools supporting the systematic and

Declarative meta-programming is vital, since it is the most promising means by which programs can be made to reason about other programs. A metaprogram is a program that takes another program, called the object program, as data. A declarative programming language is a programming language based on a logic that has a model theory. A meta-program operates on a representation of an object...

Scopo di questo articolo e` dare una panoramica introduttiva alla deduzione automatica, mettendo in evidenza obiettivi, differenze e similitudini di alcuni fra i piu` importanti approcci al problema.