A Logic-based Approach for Recognizing Textual Entailment Supported by Ontological Background Knowledge

We present the architecture and the evaluation of a new system for recognizing textual entailment (RTE). In RTE we want to identify automatically the type of a logical relation between two input texts. In particular, we are interested in proving the existence of an entailment between them. We conceive our system as a modular environment allowing for a high-coverage syntactic and semantic text analysis combined with logical inference. For the syntactic and semantic analysis we combine a deep semantic analysis with a shallow one supported by statistical models in order to increase the quality and the accuracy of results. For RTE we use logical inference of first-order employing model-theoretic techniques and automated reasoning tools. The inference is supported with problem-relevant background knowledge extracted automatically and on demand from external sources like, e.g., WordNet, YAGO, and OpenCyc, or other, more experimental sources with, e.g., manually defined presupposition resolutions, or with axiomatized general and common sense knowledge. The results show that fine-grained and consistent knowledge coming from diverse sources is a necessary condition determining the correctness and traceability of results.Comment: 25 pages, 10 figure

Logical Step-Indexed Logical Relations

Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. However, proofs using step-indexed models typically involve tedious, error-prone, and proof-obscuring step-index arithmetic, so it is important to develop clean, high-level, equational proof principles that avoid mention of step indices. In this paper, we show how to reason about binary step-indexed logical relations in an abstract and elegant way. Specifically, we define a logic LSLR, which is inspired by Plotkin and Abadi's logic for parametricity, but also supports recursively defined relations by means of the modal "later" operator from Appel, Melli\`es, Richards, and Vouillon's "very modal model" paper. We encode in LSLR a logical relation for reasoning relationally about programs in call-by-value System F extended with general recursive types. Using this logical relation, we derive a set of useful rules with which we can prove contextual equivalence and approximation results without counting steps

Liquid Clocks - Refinement Types for Time-Dependent Stream Functions

The concept of liquid clocks introduced in this paper is a significant step towards a more precise compile-time framework for the analysis of synchronous and polychromous languages. Compiling languages such as Lustre or SIGNAL indeed involves a number of static analyses of programs before they can be synthesized into executable code, e.g., synchronicity class characterization, clock assignment, static scheduling or causality analysis. These analyses are often equivalent to undecidable problems, necessitating abstracting such programs to provide sound yet incomplete analyses. Such abstractions unfortunately often lead to the rejection of programs that could very well be synthesized into deterministic code, provided abstraction refinement steps could be applied for more accurate analysis. To reduce the false negatives occurring during the compilation process, we leverage recent advances in type theory -- with the definition of decidable classes of value-dependent type systems -- and formal verification, linked to the development of efficient SAT/SMT solvers, to provide a type-theoretic approach that considers all the above analyses as type inference problems. In order to simplify the exposition of our new approach in this paper, we define a refinement type system for a minimalistic, synchronous, stream-processing language to concisely represent, analyse, and verify logical and quantitative properties of programs expressed as stream-processing data-flow networks. Our type system provides a new framework to represent logical time (clocks) and scheduling properties, and to describe their relations with stream values and, possibly, other quantas. We show how to analyze synchronous stream processing programs (à la Lustre, Signal) to enable previously described analyzes involved in compiling such programs. We also prove the soundness of our type system and elaborate on the adaptability of this core framework by outlining its extensibility to specific models of computations and other quantas

Understanding Science Through Knowledge Organizers: An Introduction

We propose, in this paper, a teaching program based on a grammar of scientific language borrowed mostly from the area of knowledge representation in computer science and logic. The paper introduces an operationizable framework for understanding knowledge using knowledge representation (KR) methodology. We start with organizing concepts based on their cognitive function, followed by assigning valid and authentic semantic relations to the concepts. We propose that in science education, students can understand better if they organize their knowledge using the KR principles. The process, we claim, can help them to align their conceptual framework with that of experts which we assume is the goal of science education