With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability of current models to capture logical operations such as negation. As a solution we propose a tripartite formulation for a continuous vector space representation of semantics and subsequently use this representation to develop a formal compositional notion of negation within such models.
The first class of approaches seeks to use distributional models of word semantics to enhance logic-based models of textual inference. The work which best exemplifies this strand of research is found in the efforts of and, more recently, . This line of research converts logical representations obtained from syntactic parses using Bos' Boxer @cite_21 into Markov Logic Networks @cite_2 , and uses distributional semantics-based models such as that of to deal with issues polysemy and ambiguity.
@cite_21 @cite_2
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We present an inference algorithm that organizes observed words (tokens) into structured inflectional paradigms (types). It also naturally predicts the spelling of unobserved forms that are missing from these paradigms, and discovers inflectional principles (grammar) that generalize to wholly unobserved words. Our Bayesian generative model of the data explicitly represents tokens, types, inflections, paradigms, and locally conditioned string edits. It assumes that inflected word tokens are generated from an infinite mixture of inflectional paradigms (string tuples). Each paradigm is sampled all at once from a graphical model, whose potential functions are weighted finite-state transducers with language-specific parameters to be learned. These assumptions naturally lead to an elegant empirical Bayes inference procedure that exploits Monte Carlo EM, belief propagation, and dynamic programming. Given 50--100 seed paradigms, adding a 10-million-word corpus reduces prediction error for morphological inflections by up to 10 . The distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs) and ProbLog. When a program contains functions symbols, the distribution semantics is well-defined only if the set of explanations for a query is finite and so is each explanation. Welldefinedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper we identify a larger class of programs for which the semantics is well-defined together with an efficient procedure for computing the probability of queries. Since LPADs offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols. We present an approach to learning a model-theoretic semantics for natural language tied to Freebase. Crucially, our approach uses an open predicate vocabulary, enabling it to produce denotations for phrases such as "Republican front-runner from Texas" whose semantics cannot be represented using the Freebase schema. Our approach directly converts a sentence's syntactic CCG parse into a logical form containing predicates derived from the words in the sentence, assigning each word a consistent semantics across sentences. This logical form is evaluated against a learned probabilistic database that defines a distribution over denotations for each textual predicate. A training phase produces this probabilistic database using a corpus of entity-linked text and probabilistic matrix factorization with a novel ranking objective function. We evaluate our approach on a compositional question answering task where it outperforms several competitive baselines. We also compare our approach against manually annotated Freebase queries, finding that our open predicate vocabulary enables us to answer many questions that Freebase cannot. We propose a new approach to semantic parsing that is not constrained by a fixed formal ontology and purely logical inference. Instead, we use distributional semantics to generate only the relevant part of an on-the-fly ontology. Sentences and the on-the-fly ontology are represented in probabilistic logic. For inference, we use probabilistic logic frameworks like Markov Logic Networks (MLN) and Probabilistic Soft Logic (PSL). This semantic parsing approach is evaluated on two tasks, Textual Entitlement (RTE) and Textual Similarity (STS), both accomplished using inference in probabilistic logic. Experiments show the potential of the approach.