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.
Boxer is an open-domain software component for semantic analysis of text, based on Combinatory Categorial Grammar (CCG) and Discourse Representation Theory (DRT). Used together with the CC (b) discourse structure triggered by conditionals, negation or discourse adverbs was overall correctly computed; (c) some measure and time expressions are correctly analysed, others aren't; (d) several shallow analyses are given for lexical phrases that require deep analysis; (e) bridging references and pronouns are not resolved in most cases. Boxer is distributed with the C&C tools and freely available for research purposes. We propose a simple approach to combining first-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a first-order knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a first-order formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudo-likelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach.