2,100 research outputs found
A Framework for Program Development Based on Schematic Proof
Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach
Logical Reduction of Metarules
International audienceMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperform subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times
Learning programs by learning from failures
We describe an inductive logic programming (ILP) approach called learning
from failures. In this approach, an ILP system (the learner) decomposes the
learning problem into three separate stages: generate, test, and constrain. In
the generate stage, the learner generates a hypothesis (a logic program) that
satisfies a set of hypothesis constraints (constraints on the syntactic form of
hypotheses). In the test stage, the learner tests the hypothesis against
training examples. A hypothesis fails when it does not entail all the positive
examples or entails a negative example. If a hypothesis fails, then, in the
constrain stage, the learner learns constraints from the failed hypothesis to
prune the hypothesis space, i.e. to constrain subsequent hypothesis generation.
For instance, if a hypothesis is too general (entails a negative example), the
constraints prune generalisations of the hypothesis. If a hypothesis is too
specific (does not entail all the positive examples), the constraints prune
specialisations of the hypothesis. This loop repeats until either (i) the
learner finds a hypothesis that entails all the positive and none of the
negative examples, or (ii) there are no more hypotheses to test. We introduce
Popper, an ILP system that implements this approach by combining answer set
programming and Prolog. Popper supports infinite problem domains, reasoning
about lists and numbers, learning textually minimal programs, and learning
recursive programs. Our experimental results on three domains (toy game
problems, robot strategies, and list transformations) show that (i) constraints
drastically improve learning performance, and (ii) Popper can outperform
existing ILP systems, both in terms of predictive accuracies and learning
times.Comment: Accepted for the machine learning journa
Combining Forward and Backward Abstract Interpretation of Horn Clauses
Alternation of forward and backward analyses is a standard technique in
abstract interpretation of programs, which is in particular useful when we wish
to prove unreachability of some undesired program states. The current
state-of-the-art technique for combining forward (bottom-up, in logic
programming terms) and backward (top-down) abstract interpretation of Horn
clauses is query-answer transformation. It transforms a system of Horn clauses,
such that standard forward analysis can propagate constraints both forward, and
backward from a goal. Query-answer transformation is effective, but has issues
that we wish to address. For that, we introduce a new backward collecting
semantics, which is suitable for alternating forward and backward abstract
interpretation of Horn clauses. We show how the alternation can be used to
prove unreachability of the goal and how every subsequent run of an analysis
yields a refined model of the system. Experimentally, we observe that combining
forward and backward analyses is important for analysing systems that encode
questions about reachability in C programs. In particular, the combination that
follows our new semantics improves the precision of our own abstract
interpreter, including when compared to a forward analysis of a
query-answer-transformed system.Comment: Francesco Ranzato. 24th International Static Analysis Symposium
(SAS), Aug 2017, New York City, United States. Springer, Static Analysi
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