Mathematical Foundations for a Compositional Distributional Model of Meaning

We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.Comment: to appea

Combining Luhmann and Actor-Network Theory to see Farm Enterprises as Self-organizing Systems

From a rural, sociological point of view no social theories have so far been able to grasp the ontological complexity and special character of a farm enterprise as an entity in a really satisfying way. The contention of this paper is that a combination of Luhmann’s theory of social systems and the actor-network theory (ANT) of Latour, Callon, and Law offers a new and radical framework for understanding a farm as a self-organizing, heterogeneous system. Luhmann’s theory offers an approach to understand a farm as a self-organizing system (operating in meaning) that must produce and reproduce itself through demarcation from the surrounding world by selection of meaning. The meaning of the system is expressed through the goals, values, and logic of the farming processes. This theory is, however, less useful when studying the heterogeneous character of a farm as a mixture of biology, sociology, technology, and economy. ANT offers an approach to focus on the heterogeneous network of interactions of human and non-human actors, such as knowledge, technology, money, farmland, animals, plants, etc., and how these interactions depend on both the quality of the actors and the network context of interaction. But the theory is weak when it comes to explaining the self-organizing character of a farm enterprise. Using Peirce’s general semiotics as a platform, the two theories in combination open a new and radical framework for multidisciplinary studies of farm enterprises that may serve as a platform for communication between the different disciplines and approaches

Three Concepts of Law: The Ambiguous Legacy of H.L.A. Hart

The law presents itself as a body of meaning, open to discovery, interpretation, application, criticism, development and change. But what sort of meaning does the law possess? Legal theory provides three sorts of answers. The first portrays the law as a mode of communication through which law-makers convey certain standards or norms to the larger community. The law's meaning is that imparted by its authors. On this view, law is a vehicle, conveying a message from a speaker to an intended audience. The second theory portrays the law as a mode of interpretation, whereby judges, officials, and ordinary citizens make decisions about how the law applies in various practical contexts. The law's meaning is that furnished by its interpreters. According to this theory, law is a receptacle into which decision-makers pour meaning. The third viewpoint argues that these theories, while not altogether wrong, are incomplete because they downplay or ignore the autonomous meaning that the law itself possesses. This theory suggests that the law is basically a mode of participation, whereby legislators, judges, officials, and ordinary people attune themselves to an autonomous field of legal meaning. The law's meaning is grounded in a body of social practice which is independent of both the law's authors and its interpreters and which is infused with basic values and principles that transcend the practice. On this view, law is the emblem of meaning that lies beyond it. Elements of all three theories are present in H.L.A. Hart's influential work, The Concept of Law, which attempts to fuse them into a single, all-encompassing theory. Nevertheless, as we will argue here, the attempt is not successful. Any true reconciliation of the communication and interpretation theories can only take place within the framework of a fully developed participation theory. In the early stages of his work, Hart lays the foundation for such a theory. However, his failure to elaborate it in a thoroughgoing way renders the work incomplete and ultimately unbalanced. As we will see, there is something to be learned from this failure

An Algebraic Framework for Compositional Program Analysis

The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program is computed by dividing it into sub-programs, computing their meaning, and then combining the results. Compositional program analyses are desirable because they can yield scalable (and easily parallelizable) program analyses. This paper presents algebraic framework for designing, implementing, and proving the correctness of compositional program analyses. A program analysis in our framework defined by an algebraic structure equipped with sequencing, choice, and iteration operations. From the analysis design perspective, a particularly interesting consequence of this is that the meaning of a loop is computed by applying the iteration operator to the loop body. This style of compositional loop analysis can yield interesting ways of computing loop invariants that cannot be defined iteratively. We identify a class of algorithms, the so-called path-expression algorithms [Tarjan1981,Scholz2007], which can be used to efficiently implement analyses in our framework. Lastly, we develop a theory for proving the correctness of an analysis by establishing an approximation relationship between an algebra defining a concrete semantics and an algebra defining an analysis.Comment: 15 page

Combining Luhmann and Actor-Network Theory to see Farm Enterprises as Self-organizing Systems

From a rural, sociological point of view no social theories have so far been able to grasp the ontological complexity and special character of a farm enterprise as an entity in a really satisfying way. The contention of this paper is that a combination of Luhmann’s theory of social systems and actor-network theory (ANT) of Latour, Callon, and Law offers a new and radical framework for understanding a farm as a self-organizing, heterogeneous system. Luhmann’s theory offers an approach to understand a farm as a self-organizing system (operating in meaning) that must produce and reproduce itself through demarcation from the surrounding world by selection of meaning. The meaning of the system is expressed through the goals, values, and the logic of the farming processes. His theory, however, is less useful when studying the heterogeneous character of a farm as a mixture of biology, sociology, technology, and economy. ANT offers an approach to focus on the heterogeneous network of interactions of human and non-human actors such as knowledge, technology, money, farmland, animals, plants, etc., and as to how these interactions depend on both the quality of the actors and the network context of interaction, but the theory is weak when it comes to explaining the self-organizing character of a farm enterprise

Dimensions of social meaning in post-classical Greek towards an integrated approach

Especially in the first half of the twentieth century, language was viewed as a vehicle for the transmission of facts and ideas. Later on, scholars working in linguistic frameworks such as Functional and Cognitive Linguistics, (Historical) Sociolinguistics and Functional Sociolinguistics, have emphasized the social relevance of language, focusing, for example, on linguistic concepts such as deixis, modality, or honorific language, or embedding larger linguistic patterns in their social contexts, through notions such as register, sociolect, genre, etc. The main aim of this article is to systematize these observations, through an investigation of how the central, though ill-understood notion of “social meaning” can be captured. The starting point for the discussion is the work that has been done in the framework of Systemic Functional Linguistics. This framework distinguishes “social” (“interpersonal”) meaning from two other types of meaning, and offers a typology of different types of contexts with which these different meanings resonate. In order to achieve a more satisfactory account of social meaning, however, I argue that we need to connect to a theory of how signs convey meaning. The discussion is relevant for Ancient Greek in its entirety, but focuses specifically on Post-classical Greek: as a case study, I discuss five private letters from the so-called Theophanes archive

Finite groups in Axiomatic Index Number Theory

In this paper we adopt Group Theory to investigate the symmetry and invariance properties of price index numbers. An alternative treatment is given to the study of the reversibilty axioms, that clarifies their meaning and allows for a conceptual unification of this topic, within the framework of Axiomatic Index Number Theory.Price index, Axiomatic Index Number Theory, Basis antithesis, Factor antithesis, Group Theory