Redundancy and subsumption in high-level replacement systems

System verification in the broadest sense deals with those semantic properties that can be decided or deduced by analyzing a syntactical description of the system. Hence, one may consider the notions of redundancy and subsumption in this context as they are known from the area of rule-based systems. A rule is redundant if it can be removed without affecting the semantics of the system; it is subsumed by another rule if each application of the former one can be replaced by an application of the latter one with the same effect. In this paper, redundancy and subsumption are carried over from rule-based systems to high-level replacement systems, which in turn generalize graph and hypergraph grammars. The main results presented in this paper are a characterization of subsumption and a sufficient condition for redundancy, which involves composite productions.Postprint (published version

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

A theory of resolution

We review the fundamental resolution-based methods for first-order theorem proving and present them in a uniform framework. We show that these calculi can be viewed as specializations of non-clausal resolution with simplification. Simplification techniques are justified with the help of a rather general notion of redundancy for inferences. As simplification and other techniques for the elimination of redundancy are indispensable for an acceptable behaviour of any practical theorem prover this work is the first uniform treatment of resolution-like techniques in which the avoidance of redundant computations attains the attention it deserves. In many cases our presentation of a resolution method will indicate new ways of how to improve the method over what was known previously. We also give answers to several open problems in the area

Set-Theoretic Types for Polymorphic Variants

Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a type system whose behaviour is in some cases unintuitive and/or unduly restrictive. In this work, we present an alternative formalization of poly-morphic variants, based on set-theoretic types and subtyping, that yields a cleaner and more streamlined system. Our formalization is more expressive than the current one (it types more programs while preserving type safety), it can internalize some meta-theoretic properties, and it removes some pathological cases of the current implementation resulting in a more intuitive and, thus, predictable type system. More generally, this work shows how to add full-fledged union types to functional languages of the ML family that usually rely on the Hindley-Milner type system. As an aside, our system also improves the theory of semantic subtyping, notably by proving completeness for the type reconstruction algorithm.Comment: ACM SIGPLAN International Conference on Functional Programming, Sep 2016, Nara, Japan. ICFP 16, 21st ACM SIGPLAN International Conference on Functional Programming, 201

A closer look at declarative interpretations

AbstractThree semantics have been proposed as the most promising candidates for a declarative interpretation for logic programs and pure Prolog programs: the least Herbrand model, the least term model, i.e., the C-semantics, and the I-semantics. Previous results show that a strictly increasing information ordering between these semantics exists for the class of all programs. In particular, the I-semantics allows us to model the computed answer substitutions, which is not the case for the other two.We study here the relationship between these three semantics for specific classes of programs. We show that for a large class of programs (which is Turing complete), these three semantics are isomorphic. As a consequence, given a query, we can extract from the least Herbrand model of a program in this class all computed answer substitutions. However, for specific programs the least Herbrand model is tedious to construct and reason about because it contains “ill-typed” facts. Therefore, we propose a fourth semantics that associates with a “correctly typed” program the “well-typed” subset of its least Herbrand model. This semantics is used to reason about partial correctness and absence of failures of correctly typed programs. The results are extended to programs with arithmetic

Privacy-Preserving Ontology Publishing for EL Instance Stores: Extended Version

We make a first step towards adapting an existing approach for privacypreserving publishing of linked data to Description Logic (DL) ontologies. We consider the case where both the knowledge about individuals and the privacy policies are expressed using concepts of the DL EL, which corresponds to the setting where the ontology is an EL instance store. We introduce the notions of compliance of a concept with a policy and of safety of a concept for a policy, and show how optimal compliant (safe) generalizations of a given EL concept can be computed. In addition, we investigate the complexity of the optimality problem