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Lawrence S. Moss

Publications and source records attributed to Lawrence S. Moss.

29 records · Page 2Linked to original sources

Probing Natural Language Inference Models through Semantic Fragments

Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word substitutions in sentential contexts)? While such phenomena are involved in natural language inference (NLI) and go beyond basic linguistic understanding, it is unclear the extent to which they are captured in existing NLI benchmarks and effectively learned by models. To investigate this, we propose the use of semantic fragments---systematically generated datasets that each target a different semantic phenomenon---for probing, and efficiently improving, such capabilities of linguistic models. This approach to creating challenge datasets allows direct control over the semantic diversity and complexity of the targeted linguistic phenomena, and results in a more precise characterization of a model's linguistic behavior. Our experiments, using a library of 8 such semantic fragments, reveal two remarkable findings: (a) State-of-the-art models, including BERT, that are pre-trained on existing NLI benchmark datasets perform poorly on these new fragments, even though the phenomena probed here are central to the NLI task. (b) On the other hand, with only a few minutes of additional fine-tuning---with a carefully selected learning rate and a novel variation of "inoculation"---a BERT-based model can master all of these logic and monotonicity fragments while retaining its performance on established NLI benchmarks.

cs.CL↗

MonaLog: a Lightweight System for Natural Language Inference Based on Monotonicity

We present a new logic-based inference engine for natural language inference (NLI) called MonaLog, which is based on natural logic and the monotonicity calculus. In contrast to existing logic-based approaches, our system is intentionally designed to be as lightweight as possible, and operates using a small set of well-known (surface-level) monotonicity facts about quantifiers, lexical items and tokenlevel polarity information. Despite its simplicity, we find our approach to be competitive with other logic-based NLI models on the SICK benchmark. We also use MonaLog in combination with the current state-of-the-art model BERT in a variety of settings, including for compositional data augmentation. We show that MonaLog is capable of generating large amounts of high-quality training data for BERT, improving its accuracy on SICK.

cs.CL↗

Proceedings Seventeenth Conference on Theoretical Aspects of Rationality and Knowledge

This is the proceedings of the Seventeenth conference on Theoretical Aspects of Rationality and Knowledge, 17-19 July 2019, Institut de Recherche en Informatique de Toulouse (IRIT), Toulouse University Toulouse, France. The mission of the TARK conferences is to bring together researchers from a wide variety of fields, including Artificial Intelligence, Cryptography, Distributed Computing, Economics and Game Theory, Linguistics, Philosophy, and Psychology, in order to further our understanding of interdisciplinary issues involving reasoning about rationality and knowledge.

cs.GT↗

Syllogistic Logic with Cardinality Comparisons, On Infinite Sets

This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are $y$}, {\sf There are at least as many $x$ as $y$}, and {\sf There are more $x$ than $y$}. Here $x$ and $y$ range over subsets (not elements) of a given \emph{infinite} set. Moreover, $x$ and $y$ may appear complemented (i.e., as $\overset{-}{x}$ and $\overset{-}{y}$), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. There are efficient algorithms for proof search and model construction.

math.LO↗

Majority Digraphs

A majority digraph is a finite simple digraph $G=(V,\to)$ such that there exist finite sets $A_v$ for the vertices $v\in V$ with the following property: $u\to v$ if and only if "more than half of the $A_u$ are $A_v$". That is, $u\to v$ if and only if $ |A_u \cap A_v | > \frac{1}{2} \cdot |A_u|$. We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change $\frac{1}{2}$ to any real number $α\in (0,1)$, we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions "most $X$ are $Y$" and the standard connectives of propositional logic.

math.CO↗

Eigenvalues and Transduction of Morphic Sequences: Extended Version

We study finite state transduction of automatic and morphic sequences. Dekking proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called alpha-substitutivity. Roughly, a sequence is alpha-substitutive if the sequence can be obtained as the limit of iterating a substitution with dominant eigenvalue alpha. Our results culminate in the following fact: for multiplicatively independent real numbers alpha and beta, if v is an alpha-substitutive sequence and w is a beta-substitutive sequence, then v and w have no common non-erasing transducts except for the ultimately periodic sequences. We rely on Cobham's theorem for substitutions, a recent result of Durand.

cs.FL↗

The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing

We begin by discussing the history of quantum logic, dividing it into three eras or lives. The first life has to do with Birkhoff and von Neumann's algebraic approach in the 1930's. The second life has to do with attempt to understand quantum logic as logic that began in the late 1950's and blossomed in the 1970's. And the third life has to do with recent developments in quantum logic coming from its connections to quantum computation. We discuss our own work connecting quantum logic to quantum computation (viewing quantum logic as the logic of quantum registers storing qubits), and make some speculations about mathematics based on quantum principles.

math.LO↗

Automatic Sequences and Zip-Specifications

We consider infinite sequences of symbols, also known as streams, and the decidability question for equality of streams defined in a restricted format. This restricted format consists of prefixing a symbol at the head of a stream, of the stream function `zip', and recursion variables. Here `zip' interleaves the elements of two streams in alternating order, starting with the first stream. For example, the Thue-Morse sequence is obtained by the `zip-specification' {M = 0 : X, X = 1 : zip(X,Y), Y = 0 : zip(Y,X)}. Our analysis of such systems employs both term rewriting and coalgebraic techniques. We establish decidability for these zip-specifications, employing bisimilarity of observation graphs based on a suitably chosen cobasis. The importance of zip-specifications resides in their intimate connection with automatic sequences. We establish a new and simple characterization of automatic sequences. Thus we obtain for the binary zip that a stream is 2-automatic iff its observation graph using the cobasis (hd,even,odd) is finite. The generalization to zip-k specifications and their relation to k-automaticity is straightforward. In fact, zip-specifications can be perceived as a term rewriting syntax for automatic sequences. Our study of zip-specifications is placed in an even wider perspective by employing the observation graphs in a dynamic logic setting, leading to an alternative characterization of automatic sequences. We further obtain a natural extension of the class of automatic sequences, obtained by `zip-mix' specifications that use zips of different arities in one specification. We also show that equivalence is undecidable for a simple extension of the zip-mix format with projections like even and odd. However, it remains open whether zip-mix specifications have a decidable equivalence problem.

cs.LO↗

The Category Theoretic Solution of Recursive Program Schemes

This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with "enough final coalgebras" we show how to formulate, solve, and study recursive program schemes. Our general theory is algebraic and so avoids using ordered, or metric structures. Our work generalizes the previous approaches which do use this extra structure by isolating the key concepts needed to study substitution in infinite trees, including second-order substitution. As special cases of our interpreted solutions we obtain the usual denotational semantics using complete partial orders, and the one using complete metric spaces. Our theory also encompasses implicitly defined objects which are not usually taken to be related to recursive program schemes. For example, the classical Cantor two-thirds set falls out as an interpreted solution (in our sense) of a recursive program scheme.

cs.LO↗

Logics for the Relational Syllogistic

The Aristotelian syllogistic cannot account for the validity of many inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio ad absurdum is needed. Thus our main goal is to derive results on the existence (or non-existence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments.

cs.LO↗