Online research in philosophy

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts.

All sorts of things are context-dependent in one way or another. What it is appropriate to wear, to give, or to reveal depends on the context. Whether or not it is all right to lie, harm, or even kill depends on the context. If you google the phrase ‘depends on the context’, you’ll get several hundred million results. This chapter aims to narrow that down. In this context the topic is context dependence in language and its use. It is commonly observed that the same sentence can be used to convey different things in different contexts. That is why people complain when something they say is ‘taken out of context’ and insist that it be ‘put into context’, because ‘context makes it clear’ what they meant. Indeed, it is practically a platitude that what a speaker means in uttering a certain sentence, as well as how her audience understands her, ‘depends on the context’. But just what does that amount to, and to what extent is it true?

The notion of context arises in assorted areas of artificial intelligence (AI), including knowledge representation, natural language processing, intelligent information retrieval, etc. Although the term ‘context’ is frequently employed in descriptions, explanations, and analyses of computer programs in these areas, its meaning is frequently left to the reader’s understanding. In other words, it is used in an intuitive manner. In an influential paper, Clark and Carlson (1981) state that context has become a favourite word. They then complain that the denotation of the word has become murkier as its uses have been extended in many directions, making context some sort of ‘conceptual garbage can.’.

In this paper, an objective conception of contexts based loosely upon situation theory is developed and formalized. Unlike subjective conceptions, which take contexts to be something like sets of beliefs, contexts on the objective conception are taken to be complex, structured pieces of the world that (in general) contain individuals, other contexts, and propositions about them. An extended first-order language for this account is developed. The language contains complex terms for propositions, and the standard predicate "ist" that expresses the relation that holds between a context and a proposition just in case the latter is true in the former. The logic for the objective conception features a global classical predicate calculus, a local logic for reasoning within contexts, and axioms for propositions. The specter of paradox is banished from the logic by allowing "ist" to be nonbivalent in problematic cases: it is not in general the case, for any context c and proposition p, that either ist(c,p) or ist(c, ¬p). An important representational capability of the logic is illustrated by proving an appropriately modified version of an illustrative theorem from McCarthy's classic Blocks World example.

Logical AI develops computer programs that represent what they know about the world primarily by logical formulas and decide what to do primarily by logical reasoning--including nonmonotonic logical reasoning. It is convenient to use logical sentences and terms whose meaning depends on context. The reasons for this are similar to what causes human language to use context dependent meanings. This note gives elements of some of the formalisms to which we have been led. Fuller treatments are in [McC93], [Guh91] and [MB94] and the references cited in the Web page [Buv95]. The first main idea is to make contexts first class objects in the logic and use the formula ist(c,p) to assert that the proposition p is true in the context c. A second idea is to formalize how propositions true in one context transform when they are moved to different but related contexts. An ability to transcend the outermost context is needed to give computer programs the ability to reason about the totality of all they have thought about so far [McC96].

This position paper argues that in addition to the familiar approach using formal contexts, there is now a need in AI to study contexts as social constructs. As a successful example of the latter approach, I draw attention to `interpretation' (in the sense of literary theory), viz. the reconstruction of intended meaning of a literary text that takes into account the context in which the author assumed the reader would place the text. An important contribution here comes from Harris (1988), enumerating the seven crucial dimensions of context: knowledge of reality, knowledge of language, and the authorial, generic, collective, specific, and textual dimensions. Finally, two thought-provoking papers in interpretation, (Barwise 1989) and (Hobbs 1990), are analyzed as useful attempts which also come to grips with the notion of context.

Based on the premise that what is relevant, consistent, or true may change from context to context, a formal framework of relevance and context is proposed in which • contexts are mathematical entities • each context has its own language with relevant implication • the languages of distinct contexts are connected by embeddings • inter-context deduction is supported by bridge rules • databases are sets of formulae tagged with deductive histories and the contexts they belong to • abduction and revision are supported by a notion of consistency of formulae and sets of formulae which are relative to a context, and which can, in turn, be seen as constituents of agendas.

In traditional linguistic accounts of context, one thinks of the immediate features of a speech situation, that is, a situation in which an expression is uttered. Thus, features such as time, location, speaker, hearer and preceding discourse are all parts of context. But context is a wider and more transcendental notion than what these accounts imply. For one thing, context is a relational concept relating social actions and their surroundings, relating social actions, relating individual actors and their surroundings, and relating the set of individual actors and their social actions to their surroundings.

We focus on how we should define the relevance of information to a context for information processing agents, such as oracles. We build our formalization of relevance upon works in pragmatics which refer to contextual information without giving any explicit representation of context. We use a formalization of context (due to us) in Situation Theory, and demonstrate its power in this task. We also discuss some computational aspects of this formalization.

The issue of context arises in assorted areas of Artificial Intelligence. Although its importance is realized by various researchers, there is not much work towards a useful formalization. In this paper, we will present a preliminary model (based on Situation Theory) and give examples to show the use of context in various fields, and the advantages gained by the acceptance of our proposal.