LangPro is an automated theorem prover for natural language (this https URL). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic tableau method specially designed for natural logic. The proof procedure operates on logical forms that preserve linguistic expressions to a large extent. This property makes the logical forms easily obtainable from syntactic trees. , in particular, Combinatory Categorial Grammar derivation trees. The nature of proofs is deductive and transparent. On the FraCaS and SICK textual entailment datasets, the prover achieves high results comparable to state-of-the-art.
Theorem proving techniques @cite_2 or ideas from Natural Logic @cite_4 were already used in recognizing textual entailment (RTE). But the combination of these two is a novel approach to RTE. The underlying higher-order logic of guarantees sound reasoning over several premises, including some complex semantic phenomena. This is in contrast to the RTE systems that cannot reason over several premises or cannot account for Booleans and quantifiers, including the ones @cite_4 inspired by Natural Logic, and in contrast to those ones that use FOL representations and cannot cover higher-order phenomena like generalized quantifiers or subsective adjectives.
@cite_4 @cite_2
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We use logical inference techniques for recognising textual entailment. As the performance of theorem proving turns out to be highly dependent on not readily available background knowledge, we incorporate model building, a technique borrowed from automated reasoning, and show that it is a useful robust method to approximate entailment. Finally, we use machine learning to combine these deep semantic analysis techniques with simple shallow word overlap; the resulting hybrid model achieves high accuracy on the RTE testset, given the state of the art. Our results also show that the different techniques that we employ perform very differently on some of the subsets of the RTE corpus and as a result, it is useful to use the nature of the dataset as a feature. In this paper we explain how to build a recognizing textual entailment (RTE) system which only uses semantic similarity measures based on WordNet. We show how the widely used WordNet-based semantic measures can be generalized to build sentence level semantic metrics in order to be used in both mono-lingual and cross-lingual textual entailment. We experiment with a wide variety of RTE datasets and evaluate the contribution of an algorithm which expands the RTE monolingual corpus. Results achieved with this method yielded significant statistical differences when predicting RTE test sets. We provide an efficiency analysis of these metrics drawing some conclusions about their practical utility in recognizing textual entailment. We also analyze the cross-lingual textual entailment task, we create a bilingual English–Spanish corpus, and propose a procedure to create a cross-lingual textual entailment corpus for any pair of languages. Finally, we show that the proposed method is enough to build an average score RTE system in both monolingual and cross-lingual textual entailment, that uses semantic information from WordNet as the only source of lexical-semantic knowledge. We propose natural proofs for reasoning with programs that manipulate data-structures against specifications that describe the structure of the heap, the data stored within it, and separation and framing of sub-structures. Natural proofs are a subclass of proofs that are amenable to completely automated reasoning, that provide sound but incomplete procedures, and that capture common reasoning tactics in program verification. We develop a dialect of separation logic over heaps, called Dryad, with recursive definitions that avoids explicit quantification. We develop ways to reason with heaplets using classical logic over the theory of sets, and develop natural proofs for reasoning using proof tactics involving disciplined unfoldings and formula abstractions. Natural proofs are encoded into decidable theories of first-order logic so as to be discharged using SMT solvers. We also implement the technique and show that a large class of more than 100 correct programs that manipulate data-structures are amenable to full functional correctness using the proposed natural proof method. These programs are drawn from a variety of sources including standard data-structures, the Schorr-Waite algorithm for garbage collection, a large number of low-level C routines from the Glib library and OpenBSD library, the Linux kernel, and routines from a secure verified OS-browser project. Our work is the first that we know of that can handle such a wide range of full functional verification properties of heaps automatically, given pre post and loop invariant annotations. We believe that this work paves the way for deductive verification technology to be used by programmers who do not (and need not) understand the internals of the underlying logic solvers, significantly increasing their applicability in building reliable systems. The problem of deciding the satisfiability of a quantifier-free formula with respect to a background theory, also known as Satisfiability Modulo Theories (SMT), is gaining increasing relevance in verification: representation capabilities beyond propositional logic allow for a natural modeling of real-world problems (e.g., pipeline and RTL circuits verification, proof obligations in software systems). In this paper, we focus on the case where the background theory is the combination T1∪T2 of two simpler theories. Many SMT procedures combine a boolean model enumeration with a decision procedure for T1∪T2, where conjunctions of literals can be decided by an integration schema such as Nelson-Oppen, via a structured exchange of interface formulae (e.g., equalities in the case of convex theories, disjunctions of equalities otherwise). We propose a new approach for SMT(T1∪T2), called Delayed Theory Combination, which does not require a decision procedure for T1∪T2, but only individual decision procedures for T1 and T2, which are directly integrated into the boolean model enumerator. This approach is much simpler and natural, allows each of the solvers to be implemented and optimized without taking into account the others, and it nicely encompasses the case of non-convex theories. We show the effectiveness of the approach by a thorough experimental comparison.