![[*]](cross_ref_motif.gif)
is characterized schematically
in , whereby the difference is specified in terms of the
binary feature [+/-constructive].
Roland Hausser
The phenomenon of propositional attitudes raises the following question for a model-theoretic semantics of natural language:
Is the speaker-hearer part of the model structure or
is the model structure part of the speaker-hearer?
If the goal of semantics is to characterize truth, then one may use only logical meanings which are presupposed to be immediately obvious and eternal. On this approach the speaker-hearer must be part of the model structure. Thereby, the relation of truth between expressions and states of affairs exist independently of whether it is discovered by this or that speaker-hearer, or not.
If the goal is the analysis of language meaning, on the other hand, then the logical system, which was developed originally for the characterization of truth based on logical meanings, is used for a new purpose, namely the description of language meanings in the form of truth conditions. In order for the meanings of language to be used in communication by the speaker-hearer they must be part of cognition. Therefore, the analysis of natural language meanings within logical semantics leads necessarily to a reinterpretation of the model structure as something cognitive which is part of the speaker-hearer.
The alternative stated in is characterized schematically
in , whereby the difference is specified in terms of the
binary feature [+/-constructive].
The [-constructive] interpretation establishes the relation between the language surfaces and the level of referents in terms of a metalanguage. The relation exists outside the cognitive agent out there in the real world. The agent is itself an object at the level of referents, who may observe this relation between language and the objects of the world.
The [+constructive] interpretation, on the other hand, establishes the relation between the language surfaces and the level of referents solely inside the the cognitive agent in terms of cognitive procedures. What the agent does not perceive in the world plays no role in his reference procedures, though what he feels, wishes, plans, etc., does.
The most fundamental difference between the two ontologies consists in the fact that [-constructive] systems must have a metalanguage-based semantics metalanguage-based semantics while [+constructive] systems must have a procedural semantics. In [-constructive] systems, the relation between the expression and the state of affairs can only be established in terms of (meta-)language definitions because scientific statements believed to be eternally valid and independent of any speaker-hearer cannot be meaningfully operationalized. [+constructive] systems, on the other hand, are useless without a procedural semantics because neither a computer nor a cognitive agent can practically function on the basis of a metalanguage-based semantics. procedural semantics
Furthermore, a cognitive (re-)interpretation of the logical model as part the speaker-hearer is incompatible with the goals and methods of traditional theories of truth. Conversely, the `realistic' interpretation of the model within a theory of truth is incompatible with the analysis of natural language meaning.1
Another basic distinction in systems of semantic interpretation may be represented by the feature [+/-sense]. This distinction refers to the question of whether the meaning of language is identified with the objects referred to ([-sense]), or whether meaning is characterized on a separate level as a Fregean `Sinn' which is distinct from the objects referred to ([+sense]).
The features [+/-sense] and [+/-constructive] are independent of each other and can therefore be combined. This results in four types of semantic interpretation based on four different ontologies, namely [-sense, -constructive], [+sense, -constructive], [-sense,+constructive] and [+sense,+constructive].
These different ontologies have been adopted by different schools of semantic interpretation.
The [-sense,-constructive] ontology (i) is the basis of logical semantics. Concerned with a solid foundation for truth, logical semantics uses only referents which are considered to be ontologically real. In nominalism, these are the concrete signs of language and the states of affairs built up from concrete objects. In mathematical realism , the ontology is extended to include abstract objects like sets and numbers. Both versions have in common that the semantics is defined as a direct, external relation between language and the world. This type of semantics has been adopted by the main stream of modern philosophical logic, from Russell via the early Wittgenstein, Carnap, Montague, 2 to Putnam.
The [+sense,-constructive] ontology (ii) was used by Frege in his attempt to analyze uneven (opaque, intensional) readings in natural language. For modeling the mechanics of natural language communication, this type of semantics is only half a step in the right direction. As a theory of truth, any [-constructive] semantics is incompatible with representing cognitive states.3
The [-sense,+constructive] ontology (iii) is that of the semantics of programming languages. The user puts commands (surfaces of the programming language) into the computer, which turns them directly into corresponding electronic procedures. When a result has been computed, it is communicated to the user by displaying language expressions on the screen. In this traditional use, a computer is still a far cry from a cognitive agent. But there is already the important distinction between the task environment in the `world' and the computer internal problem space, whereby the semantic interpretation is located in the latter.
Because of their origin as conventional programs on conventional computers most systems of artificial intelligence are based - subconsciously, so to speak - on a [-sense,+constructive] ontology. This holds, for example, for SHRDLU (Winograd 1972), HEARSAY (Reddy et al. 1973) and SAM (Schank & Abelson 1977). In cognitive psychology this ontology has been used as well, for example in the mental models by Johnson-Laird 1983.
Within artificial intelligence, Newell & Simon 1972, p. 66, have argued explicitly against an intermediate level of sense - for purely ontological reasons. They argue that the distinction between language meanings (sense) and the computer internal referents would result ``in an unnecessary and unparsimonious multiplication of hypothetical entities that has no evidential support.''
A direct connection between language expressions and their referents, however, prevents any autonomous classification of new objects. Therefore, a [-sense,+constructive] type of semantics is limited to closed toy worlds created in advance by the programmer.4 It is by no means accidental that these systems have no components of artificial perception: because they lack the intermediate level of concepts (sense) they could not utilize perception (e.g., artificial vision) to classify and to automatically integrate new objects into their domain.
The [+sense,+constructive] ontology (iv), finally, underlies the SLIM theory of language.5 SLIM bases its [+sense] property structurally on the matching of the literal meaning and the context of use, while its [+constructive] property is based on the fact that this matching occurs inside the cognitive agent. In cognitive psychology, this type of semantics has been used by Anderson & Bower 1973 and 1980. They present a general psychological model of natural language understanding, which may be interpreted as an internal matching of language concepts onto a context structure.
The theoretical relation between the four alternative types of semantics may be analyzed by either emphasizing their ontological difference or their formal similarities. In the latter case, one will present one's semantics as a purely formal structure which may be assigned different interpretations without affecting the formal essence. For this, one may relate the different ontologies in terms of different degrees of specialization or generalization.
The difference between a [+sense] and a [-sense] ontology may be minimized by interpreting the latter as a simplification of the former. Assume that (i) the world is closed such that objects can neither appear nor disappear, (ii) the relation between language expressions and their referents is fixed once and for all, and (iii) there is no spontaneous use of language by the speaker-hearer. Then there is no reason for postulating a level of senses, thus leading to a [-sense] system as a special case of a [+sense] system.
Because of this simplification one might view the [-sense] system as more valid or more essential than the [+sense] system. One should not forget, however, that there are empirical phenomena which simply cannot be handled within a [-sense] ontology, such as the reference to new objects of a known type.
The difference between [+constructive] and a [-constructive] ontology may also be minimized in terms of a simplification. Assume that the cognitive agent has perfect recognition, such that the distinction between the external objects (i.e. language expressions and referents) and their internal cognitive representations may be neglected. Then there is no reason to distinguish between the external reality and its internal cognitive representation, thus leading to a [-constructive] ontology as a special case of a [+constructive] ontology.
Because of this simplification, one might view the [-constructive] system as more valid and more essential than the [+constructive] system. One should not forget, however, that there are empirical phenomena which simply cannot be handled within a [-constructive] ontology, such as propositional attitudes.
The choice between the four different types of semantics depends on the intended application. Therefore, when (i) expanding a given semantics to a new application or when (ii) transferring partial analyses from one application to another, one should be as well-informed about the structural differences between the four basic ontologies as about the potential formal equivalences based on simplifying abstractions.
In logic, the term proposition logical proposition has acquired a special use, representing sentences which do not require knowledge of the utterance situation for their interpretation. From the viewpoint of natural language, this is problematic because it constitutes a hybrid between an utterance (i.e. a pragmatically interpreted or interpretable token) and an expression (i.e. a pragmatically uninterpreted type). This problem shows up in the distinction between absolute and contingent propositions.
Absolute propositions express scientific or mathematical contents. For example, in the proposition
In a right-angled triangle, it holds for the hypotenuse A and the cathetes B and C that A2 = B2 + C2
the circumstances of the utterance have no influence on the interpretation and the truth value of the sentence in question, for which reason they are ignored. The special properties of absolute propositions are reflected in logical truth, formally expressed by the metalanguage words false and true referring to the abstract set-theoretic objects 0 und {0}, respectively, of the model structure.
Contingent propositions, on the other hand, are based on sentences with everyday contents such as
Your dog is doing well.
Contingent propositions can only be interpreted - and thereby evaluated with respect to their truth value - if the relevant circumstances of the utterance situation are known and systematically entered into the interpretation. This requires that the parameters of origin be known, i.e. the location, the time, the person of the speaker, and the person addressed.
The characteristic properties of contingent propositions correspond to a natural notion of truth, represented by the truth values truec and falsec. Intuitively, a contingent proposition such as natural truth
The Persians have lost the battle
may be regarded as truec, if the speaker is an eye witness who is able to correctly judge and communicate the facts, or if there exists a properly functioning chain of communication between the speaker and a reliable eye witness.
The natural truth values truec and falsec may be treated in terms of a procedural definition: A proposition - or rather a statement - uttered by a cognitive agent (e.g. a robot) is evaluated as truec, if all procedures contributing to communication work correctly. Otherwise it is evaluated as falsec.
The differences in the truth predicates of natural and logical
semantics derive from structural difference between their
respective [-sense,-constructive] and
[+sense, +constructive]
ontologies.
Both systems treat relation 5 between the external expression (sentence) and the external state of affairs as crucial for the truth of this type of statement. But they use completely different methods and concepts to realize this relation.
The [-sense,-constructive] system defines relation 5 directly by means of a suitable metalanguage metalanguage 6. The analysis is done by the logician, who - in concord with the ontology presumed - concentrates solely on the truth relation between the expression and the state of affairs, abstracting from all structural aspects of communication. The logical model and the rule based interpretation of the expression are designed to realize formally what is assumed as obvious to begin with. The purpose of the logical system is the explicit derivation of truth values.
In a [+sense, +constructive] system, on the other hand, a real task environment is given. It must be analyzed automatically by the cognitive agent in certain relevant aspects, whereby a corresponding context representation is constructed internally. Relation 5 between the language sign and the external state of affairs is thus established indirectly in terms of cognitive procedures, based on the components 1 (non-verbal cognition/action), 2 (pragmatic interpretation), 3 (semantic interpretation), and 4 (verbale cognition/action). The purpose of the system is not a characterization of truth, but rather the communicating of contextual contents by means of language.
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