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Elio Lanzarone: A life for science
Abstract
We are sincerely grateful to have been invited by the Guest Editor of this special issue, Prof. Francesca Lisi, to write an article in honor of our mentor Gaetano Aurelio Lanzarone (for students, colleagues and friends simply 'Elio'). We were the first (Stefania) and last (Federico) of Elio's students, and we both entertained a particularly deep relation with him. What we want to do here is to provide a memoir of his life and career, while his smile, laughter and humor cannot be described in words, but only in the language of our hearts and memories. We believe that Elio's attitude towards life is well described by the words that Dante Alighieri in his 'Divina Commedia' (Divine Comedy, Inferno [Hell], Chant XXVI) attributes to Ulysses:
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This paper presents a logic programming language of novel conception, called Reflective Prolog, which allows declarative metaknowledge representation and metareasoning. The language is defined by augmenting pure Prolog (Horn clauses) with capabilities of self-reference and logical reflection. Self-reference is designed as a quotation device (a carefully defined naming relation) which allows the construction of metalevel terms that refer to object-level terms and atoms. Logical reflection is designed as an unquotation mechanism (a distinguished truth predicate) which relates names to what is named, thus extending the meaning of domain predicates. The reflection mechanism is embodied in an extended resolution procedure which automatically switches the context between levels. This implicit reflection relieves the programmer from having to explicitly deal with control aspects of the inference process. The declarative semantics of a Reflective Prolog definite program P is provided in terms of the least reflective Herbrand model of P, characterized by means of a suitable mapping defined over the Herbrand interpretations of P. The extended resolution is proved sound and complete with respect to the least reflective Herbrand model. By illustrating Reflective Prolog solutions to an organic set of problems, and by discussing the main differences with respect to other approaches to logic metaprogramming, we show that the proposed language deploys, within its field of action, greater expressive and inferential power than those available till now. The interpreter of the language has been fully implemented. Because of its enhanced power, logic semantics and working interpreter, Reflective Prolog is offered as a contribution toward making the declarative approach of logic programming applicable to the development of increasingly sophisticated knowledge-based systems.
A formal model of analogy is introduced in the logic programming setting, and an analogical reasoning program (called DIANA, i.e. Declarative Inference by ANAlogy) is developed in accordance with precise procedural and declarative semantics. Given the source and target domains of analogy as two logic programsP
s
andP
t
, together with a specificationS of the analogical correspondence between predicate symbols, atoms involving these symbols are analogically derived fromP=P
s P
t
givenS, which are not derivable fromP
s
orP
t
orP
s
P
t
alone. In this paper, the requirements of the analogical process are first stated. The declarative semantics of analogy is then given, by defining the least analogical model ofP as an extension of the classical semantics of Horn clauses. A procedural semantics is also described, in terms of an extension of SLD resolution. Both semantics rely on implicit analogical axioms defining the kind of analogical reasoning envisaged. The implementation of DIANA has been done in Reflective Prolog, a metalogic programming language previously developed by the first two authors. It is shown that analogical axioms can be viewed as an instance of reflection axioms used in Reflective Prolog. By exploiting this feature, the implementation of DIANA is argued to be sound w.r.t. the defined semantics. Examples of analogical reasoning in DIANA are also described. By comparison with the AI literature on analogy, it is claimed that this is the first approach which gives a declarative semantics to analogical reasoning, thanks to the possibility of carrying over in this field the basic logic programming concepts.
In this paper we discuss reasoning about reasoning in a multiple agent scenario. We consider agents that are perfect reasoners, loyal, and that can take advantage of both the knowledge and ignorance of other agents. The knowledge representation formalism we use is (full) first order predicate calculus, where different agents are represented by different theories, and reasoning about reasoning is realized via a meta-level representation of knowledge and reasoning. The framework we provide is pretty general: we illustrate it by showing a machine checked solution to the three wisemen puzzle. The agents' knowledge is organized into units: the agent's own knowledge about the world and its knowledge about other agents are units containing object-level knowledge; a unit containing meta-level knowledge embodies the reasoning about reasoning and realizes the link among units. In the paper we illustrate the meta-level architecture we propose for problem solving in a multi-agent scenario; we discuss our approach in relation to the modal one and we compare it with other meta-level architectures based on logic. Finally, we look at a class of applications that can be effectively modeled by exploiting the meta-level approach to reasoning about knowledge and reasoning.
This is an informal description of my ideas about using formal logic as a tool for reasoning systems using computers. The theoretical ideas are illustrated by the features of fol. All of the examples presented have actually run using the fol system.
Many well-known algorithms may not be expressed by means of only do-while statements. The use of newly introduced and more powerful control constructs (leave-like statements), however, gives rise to difficulties in top-down programming (specifically, the multi-level jumps problem, and the violation of the one-entry, one-exit rule). Control constructs are analyzed on the basis of the expressive power of algorithms (which is founded on previous theoretical results) and are grouped into two main families (here called 'control structures' and 'control environments'). This analysis leads to the identification of objective criteria for designing an organic set of control constructs which allows flexibility in top-down programming and avoids the above mentioned difficulties. A choice for such a set is shown, and its advantages are illustrated by recoding some well-known algorithms.
This paper deals with the problem of constructing the final version of P**t of a flowchart program through successive refinements P**2,. . . ,P**t** minus **1 that preserve correctness proved on its first version P**1. The transition from data structures on which P**i is defined to that of P**i** plus **1 is made by means of representation function that expresses the properties of such a refinement, i. e. the choices made by the programmer. On this basis, and with regard to the operations available at the successive level, each block of program P**i is expanded into a subprogram of P**i** plus **1, and the conditions are given under which such expansion is made correctly, that is according to the representation function chosen. The conditions of correct expansion therefore turn out to be useful in practice as a guide to refinement constructions, and the representation function acts as documentation of the choices made by the programmer in program construction. It is then shown that, for each level to maintain the correctness proved at the first level with respect to assigned conditions, both conditions of correct expansion and interface conditions which express the retention of the connections between blocks existing at the first level, must be satisfied.
We introduce the concept of reflection principle as a knowledge representation paradigm in a computational logic setting. Reflection principles are expressed as certain kinds of logic schemata intended to capture the basic properties of the domain knowledge to be modeled. Reflection is then used to instantiate these schemata to answer specific queries about the domain. This differs from other approaches to reflection mainly in the following three ways. First, it uses logical instead of procedural reflection. Second, it aims at a cognitively adequate declarative representation of various forms of knowledge and reasoning, as opposed to reflection as a means for controlling computation or deduction. Third, it facilitates the building of a complex theory by allowing a simpler theory to be enhanced by a compact metatheory, contrary to the construction of metatheories that are only conservative extensions of the basic theory. A computational logic system for embedding reflection principles, called RCL (for Reflective Computational Logic), is presented in full detail. The system is an extension of Horn clause resolution-based logic, and is devised in a way that makes important features of reflection parametric as much as possible, so that they can be tailored according to specific needs of different application domains. Declarative and procedural semantics of the logic are described and correctness and completeness of reflection as logical 1 inference are proved. Examples of reflection principles for three different application areas are shown. Relationship with a variety of distinct sources within the literature on relevant topics is discussed.
The theories considered here are based on the classical functional calculus (possibly of higher order) together with a set A of non-logical axioms; they are also assumed to contain classical first-order number theory. In foundational investigations it is customary to further restrict attention to the case that A is recursive, or at least recursively enumerable (an equivalent restriction, by [1]). For such axiomatic theories we have the well-known incompleteness phenomena discovered by Godei [6]. Quite far removed from such theories are those based on non-constructive sets of axioms, for example the set of all true sentences of first-order number theory. According to Tarski's theorem, there is not even an arithmetically definable set of axioms A which will give the same result (cf. [18] for exposition).
The need for expressing and using metalevel knowledge is emerging in the design of several kinds of AI systems. The careful distinction between object-level and metalevel notions and the formalization of the latter has first been carried out by logicians for foundational reasons; subsequently, the distinction has been exploited in Artificial Intelligence and Computation Theory, revealing itself to be of great relevance to Automated Deduction and Problem Solving. This paper concentrates on the use of metaknowledge in building knowledge-based systems. In order to introduce the issue, some motivating examples are presented. We then review various paradigms for combining knowledge and metaknowledge, with the aim of abstracting general criteria that should underly the construction of viable AI systems, as far as metaknowledge is concerned. Furthermore, a general overview of the uses of metaknowledge in AI is provided and, among them, we concentrate on inference control, which can be conveniently exercised by formalizing control strategies at the metalevel and by letting the inference engine depend on metalevel descriptions. The technique is presented with the aid of some examples, chosen from practical AI applications, that are expressed in the formalism of Horn clause logic. The issue of self-descriptive systems is then addressed. A system that embodies and can use an adequate description of itself allows for self-evaluation (e.g., the estimate of the resources needed to perform a given task) and for self-modification (e.g., the automatic improvement of deduction performance by profiting from experience gained in previous deductions).
In this paper we discuss a view of the machine-learning technique called Explanation-Based Learning (EBL) or Explanation-Based Generalization (EBG) as a process for the interpretation of vague concepts in logic-based models of law.