Correct-schema-guided synthesis of steadfast programs

It can be argued that for (semi-)automated software development, program schemas are indispensable, since they capture not only structured program design principles, but also domain knowledge, both of which are of crucial importance for hierarchical program synthesis. Most researchers represent schemas purely syntactically (as higher-order expressions). This means that the knowledge captured by a schema is not formalized. We take a semantic approach and show that a schema can be formalized as an open (first-order) logical theory that contains an open logic program. By using a special kind of correctness for open programs, called steadfastness, we can define and reason about the correctness of schemas. We also show how to use correct schemas to synthesize steadfast programs

Inductive logic program synthesis with dialogs

DIALOGS (Dialogue-based Inductive and Abductive LOGic program Synthesizer) is a schema-guided synthesizer of recursive logic programs; it takes the initiative and queries a (possibly computationally naive) specifier for evidence in her/his conceptual language. The specifier must know the answers to such simple queries, because otherwise s/he wouldn't even feel the need for the synthesized program. DIALOGS call be used by any learner (including itself) that detects, or merely conjectures, the necessity of invention of a new predicate. Due to its foundation on a powerful codification of a “recursion-theory” (by means of the template and constraints of a divide-and-conquer schema), DIALOGS needs very little evidence and is very fast. © Springer-Vertag Berlin Heidelberg 1997

Constructive approaches to Program Induction

Search is a key technique in artificial intelligence, machine learning and Program Induction. No matter how efficient a search procedure, there exist spaces that are too large to search effectively and they include the search space of programs. In this dissertation we show that in the context of logic-program induction (Inductive Logic Programming, or ILP) it is not necessary to search for a correct program, because if one exists, there also exists a unique object that is the most general correct program, and that can be constructed directly, without a search, in polynomial time and from a polynomial number of examples. The existence of this unique object, that we term the Top Program because of its maximal generality, does not so much solve the problem of searching a large program search space, as it completely sidesteps it, thus improving the efficiency of the learning task by orders of magnitude commensurate with the complexity of a program space search. The existence of a unique Top Program and the ability to construct it given finite resources relies on the imposition, on the language of hypotheses, from which programs are constructed, of a strong inductive bias with relevance to the learning task. In common practice, in machine learning, Program Induction and ILP, such relevant inductive bias is selected, or created, manually, by the human user of a learning system, with intuition or knowledge of the problem domain, and in the form of various kinds of program templates. In this dissertation we show that by abandoning the reliance on such extra-logical devices as program templates, and instead defining inductive bias exclusively as First- and Higher-Order Logic formulae, it is possible to learn inductive bias itself from examples, automatically, and efficiently, by Higher-Order Top Program construction. In Chapter 4 we describe the Top Program in the context of the Meta-Interpretive Learning approach to ILP (MIL) and describe an algorithm for its construction, the Top Program Construction algorithm (TPC). We prove the efficiency and accuracy of TPC and describe its implementation in a new MIL system called Louise. We support theoretical results with experiments comparing Louise to the state-of-the-art, search-based MIL system, Metagol, and find that Louise improves Metagol’s efficiency and accuracy. In Chapter 5 we re-frame MIL as specialisation of metarules, Second-Order clauses used as inductive bias in MIL, and prove that problem-specific metarules can be derived by specialisation of maximally general metarules, by MIL. We describe a sub-system of Louise, called TOIL, that learns new metarules by MIL and demonstrate empirically that the metarules learned by TOIL match those selected manually, while maintaining the accuracy and efficiency of learning. iOpen Acces

Logic Program Synthesis from Incomplete Specifications

We develop a framework for stepwise synthesis of logic programs from incomplete specifications. After the definition of logic formalisms for specifications and programs, logic program correctness and comparison criteria are proposed. Then we define criteria for upward and downward progression, in order to state strategies for incremental and non-incremental stepwise synthesis. It is shown how these strategies can be applied in practice. Finally, we instantiate the framework on a particular synthesis mechanism that we have developed. Our synthesis system, called SYNAPSe, is non-incremental, both deductive and inductive, and guided by a divide-and-conquer schema. We describe the objectives and methods of the crucial steps, and illustrate them on a sample problem