Meinongian Semantics and Artificial Intelligence

This essay describes computational semantic networks for a philosophical audience and surveys several approaches to semanticnetwork semantics. In particular, propositional semantic networks (exemplified by SNePS) are discussed; it is argued that only a fully intensional, Meinongian semantics is appropriate for them; and several Meinongian systems are presented. 1. Meinong, Philosophy, and Artificial Intelligence Philosophy was not kind to Meinong, the late-19th/early-20th-century cognitive scientist, until the 1970s renaissance in Meinong studies (Findlay, 1963; Grossmann, 1974; Rapaport, 1978; 1991b; Routley, 1979; Lambert, 1983; Schubert-Kalsi, 1987). Even so, his writings are often treated as curiosities (or worse) by mainstream philosophers. Meinong’s contribution to philosophy can be characterized in terms of his thoroughgoing intensionalism. While some philosophers ridiculed or rejected this approach, some AI researchers — for largely independent, though closely related, reasons — argued for it. Here, I explore some of their arguments and show the relevance of Meinongian theories to research in AI. 2. Semantic Networks Knowledge representation and reasoning (KRR) is an area of AI concerned with systems for representing, storing, retrieving, and inferring information in cognitively adequate and computationally efficient ways. The represented † Department of Computer Science & Engineering and Center for Cognitive Science, University at Buffalo, Buffalo, NY 14260, USA. 26 Humana.Mente – Issue 25 – December 2013 information need not necessarily be true, so a better terminology is ‘belief representation’ (Rapaport & Shapiro, 1984; Rapaport, 1986b; 1992; Rapaport et al. 1997). A semantic network is a representational system consisting of a labeled, directed graph whose “nodes” (vertices) represent objects and whose “arcs” (edges, or “links”, or “pointers”) represent binary relations among them (Findler, 1979; Brachman & Levesque, 1985; Sowa, 1991; 1992; 2002; Lehmann, 1992). Woods (1975, p. 44) says, “The major characteristic of the semantic networks that distinguishes them from other candidates [for KR systems] is the characteristic notion of a link or pointer which connects individual facts into a total structure.” Quillian’s (1967; 1968; 1969) early “semantic memory” introduced semantic networks as a model of associative memory: Nodes represented words and meanings; arcs represented “associative links” among these. The “full concept” of a word w was the entire network of nodes and arcs reachable by following directed arcs originating at the node representing w. Inheritance (or hierarchical) networks use such arc labels as “inst[ance]”, “isa”, and “property” to represent taxonomic structures (Bobrow &Winograd, 1977; Charniak & McDermott, 1985, pp. 22–27; Thomason, 1992; Brachman & Levesque, 2004, ch. 10; see Fig. 1). Schank’s Conceptual Dependency representational scheme uses nodes to represent conceptual primitives, and arcs to represent dependencies and semantic case relations among them (Schank & Rieger, 1974; Brand, 1984, ch. 8; Rich & Knight, 1991, pp. 277– 288; Hardt, 1992; Lytinen 1992). The idea is an old one: Networks like those of Quillian, and Bobrow & Winograd’s KRL (1977), or Brachman’s KL-ONE (Brachman, 1979; Brachman & Schmolze, 1985; Woods & Schmolze, 1992; and subsequent “description logics” — Brachman & Levesque, 2004, ch. 9) bear strong family resemblances to “Porphyry’s Tree” (Fig. 2) — the mediaeval device used to illustrate the Aristotelian theory of definition by species and differentia. Meinongian Semantics and Artificial Intelligence 27 Figure 1: An inheritance network representing the propositions: Tweety is (an instance of) a canary; Opus is (an instance of) a penguin; A canary is a bird; A penguin is a bird; A canary can (i.e., has the property of being able to) sing; A penguin can’t (i.e., has the property of not being able to) fly; A bird is an animal; A bird can fly; A bird has feathers; An animal has skin. However, the precise representations cannot be determined unambiguously from the network without a clearly specified syntax and semantics. Figure 2: Porphyry’s Tree: A mediaeval inheritance network (From Sowa 2002). 28 Humana.Mente – Issue 25 – December 2013 3. Semantics of Semantic Networks Semantic networks are not essentially “semantic” (Hendrix, 1979; but cf. Woods, 1975; Brachman, 1979). Viewed as a data structure, a semantic network is a language (possibly with an associated logic or inference mechanism) for representing information about some domain. As such, it is a purely syntactic entity. They are called “semantic” primarily because of their uses as ways of representing the meanings of linguistic items. (However, this sort of syntax can be viewed as a kind of semantics, as in the so-called “Semantic Web”; cf. Rapaport 1988; 2000; 2003; 2012.) As a notational device, a semantic network can itself be given a semantics. I.e., the arcs and nodes of a semantic-network representational system can be given interpretations in terms of the entities they are used to represent. Without such a semantics, a semantic network is an arbitrary notational device liable to misinterpretation (Woods, 1975; Brachman, 1977; 1983; and, especially, McDermott, 1981). E.g., in an inheritance network like that of Figure 1, how is the inheritance of properties to be represented or — more importantly — blocked? (If flying is a property inherited by the canary Tweety in virtue of its being a bird, what is to prevent the property of flying from being inherited by the flightless penguin Opus?) Do nodes represent classes of objects, types of objects, individual objects, or something else? Can arcs be treated as objects (perhaps with (“meta-”)arcs linking them in some fashion)? Providing a semantics for semantic networks is more akin to providing one for a language than for a logic. In the latter case, but not the former, notions like argument validity must be established, and connections must be made with axioms and rules of inference, culminating ideally in soundness and completeness theorems. But underlying the logic’s semantics there must be a semantics for the logic’s underlying language; this would be given in terms of such a notion as meaning. Typically, an interpretation function is established between syntactical items from the language L and ontological items from the “world” W that the language is to describe. This is usually accomplished by describing the world in another language, LW, and showing that L and LW are notational variants by showing (ideally) that they are isomorphic. Linguists and philosophers have argued for the importance of intensional semantics for natural languages (Montague, 1974; Parsons, 1980, Rapaport, 1981). At the same time, computational linguists and other AI researchers have recognized the importance of representing intensional entities (Woods, Meinongian Semantics and Artificial Intelligence 29 1975; Brachman, 1979; McCarthy, 1979; Maida & Shapiro, 1982; Hirst, 1991). It seems reasonable that a semantics for such a representational system should itself be an intensional semantics. In this essay, I discuss the arguments of Woods and others and outline several fully intensional semantics for intensional semantic networks by discussing the relations between a semantic-network “language” L and several candidates for LW. For L, I focus on the fully intensional, propositional Semantic Network Processing System (SNePS, [http://www.cse.buffalo.edu/sneps/]; Shapiro, 1979; 2000a; Shapiro & Rapaport, 1987; 1992; 1995), for which Israel (1983) offered a possibleworlds semantics. But possible-worlds semantics, while countenancing intensional entities, are not fully intensional: They treat intensional entities extensionally. Each LW I discuss has fully intensional components. 4. Arguments for Intensions The first major proponent of the need to represent intensional objects in semantic networks was Woods (1975). Brachman (1977) showed a way to do this. And Maida & Shapiro (1982) argued that only intensional entities should be represented. Woods (1975, pp. 38–40) characterizes linguistic semantics as the study of the relations between (a) such linguistic items as sentences and (b) meanings expressed in an unambiguous notation — an internal representation — and he characterizes philosophical semantics as the study of the relations between such a notation and truth conditions or meanings. Thus, he takes semantic networks as examples of the “range” of linguistic semantics and the “domain” of philosophical semantics. Semantic networks, then, are models of the realm of objects of thought (or, perhaps, of the “contents” of psychological acts) — i.e., of Meinong’s Aussersein. Woods (1975, p. 45) proposes three “requirements of a good semantic representation”: logical adequacy — it must “precisely, formally, and unambiguously represent any particular interpretation that a human listener may place on a sentence”; translatability — “there must be an algorithm or procedure for translating the original sentence into this representation”; and intelligent processing — “there must be algorithms which can make use of this representation for the subsequent inferences and deductions that the human or machine must perform on them”. 30 Humana.Mente – Issue 25 – December 2013 Logical adequacy constitutes one reason why semantic networks “must include mechanisms for representing propositions without commitment to asserting their truth or belief ... [and why] they must be able to represent various types of intensional objects without commitment to their existence in the external world, their external distinctness, or their completeness in covering all of the objects which are presumed to exist” (Woods, 1975, p. 36f). Some sentences can be interpreted as referring to nonexistents; so, a semantic network ought to be able to represent this, hence must be able to represent intensional entities. (The other criteria are discussed in §5.) A second reason is that “semantic networks should not ... provide a ‘canonical form’ in which all paraphrases of a given proposition are reduced to a single standard (or canonical) form” (Woods, 1975, p. 45). Therefore, they should not represent extensional entities, which would be such canonical forms. There are three reasons why canonical forms are to be avoided. First, there aren’t any (see the argument in Woods, 1975, p. 46). Second, no computational efficiency would be gained by having them (Woods, 1975; p. 47). Third, it should not be done if one is interested in adequately representing human processing (Rapaport, 1981). Sometimes, redundant information must be stored: Even though an uncle is extensionally equivalent to a father’sbrother-or-mother’s-brother, it can be useful to be able to represent uncles directly; thus, it is not an extension, but, rather, an intension, that must be represented (cf. Woods, 1975, p. 48). A third argument for the need to represent intensional objects comes from consideration of question-answering programs (Woods, 1975: 60ff). Suppose that a “knowledge base” has been told that The dog that bit the man had rabies How would the question “Was the man bitten by a dog that had rabies?” be represented? Should a new node be created for “the dog that bit the man”? The solution is to create such a new node and then decide if it is co-referential with an already existing one. (Discourse Representation Theory uses a similar technique; Kamp & Reyle, 1993.) Finally, intensional nodes are clearly needed for the representation of verbs of propositional attitude (Woods, 1975, p. 67; Rapaport & Shapiro, 1984; Rapaport, 1986b; 1992; Wiebe & Rapaport, 1986; Rapaport et al., 1997), and they can be used in quantificational contexts to represent “variable Meinongian Semantics and Artificial Intelligence 31 entities” (Woods, 1975, p. 68ff; Fine,1983; Shapiro, 1986; 2000b; 2004; Ali & Shapiro, 1993). Maida & Shapiro (1982) claims that, although semantic networks can represent real-world (extensional) entities or linguistic items, they should, for certain purposes, only represent intensional ones, especially when representing referentially opaque contexts (e.g., belief, knowledge), the concept of a truth value (as in ‘John wondered whether P’), and questions. In general, intensional entities are needed if one is representing a mind. Why would one need extensional entities if one is representing a mind? To represent co-referentiality? No; as we shall see, this can (and perhaps only can) be done using only intensional items. To talk about extensional entities? But why would one want to? Everything that a mind thinks or talks about is an (intenTional) object of thought, hence intenSional. (Rapaport, 2012, §3.1, surveys arguments for this “narrow” or “internal” perspective.) In order to link the mind to the actual world (to avoid solipsistic representationalism)? But consider the case of perception: There are internal representations of external objects, yet these “need not extensionally represent” those objects (Maida & Shapiro, 1982, p. 300). The “link” would be forged by connections to other intensional nodes or by consistent input-output behavior that improves over time (Rapaport, 1985/1986, pp. 84–85; Rapaport, 1988; Srihari & Rapaport, 1989; Shapiro & Rapaport, 1991 surveys the wide variety of items that can be represented by intensional entities).