Abstract
Bayesian interpretation is a technique in signal processing and its application to natural language semantics and pragmatics (BNLSP from here on and BNLI if there is no particular emphasis on semantics and pragmatics) is basically an engineering decision. It is a cognitive science hypothesis that humans emulate BNLSP. That hypothesis offers a new perspective on the logic of interpretation and the recognition of other people’s intentions in inter-human communication. The hypothesis also has the potential of changing linguistic theory, because the mapping from meaning to form becomes the central one to capture in accounts of phonology, morphology and syntax. Semantics is essentially read off from this mapping and pragmatics is essentially reduced to probability maximation within Grice’s intention recognition. Finally, the stochastic models used can be causal, thus incorporating new ideas on the analysis of causality using Bayesian nets. The paper explores and connects these different ways of being committed to BNLSP.
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Notes
- 1.
Symbolic parsing with visual grammars becomes intractable as soon as the grammar becomes interesting (Marriott and Meyer 1997). It follows that visual recognition must be stochastic. To profit fully from the mental camera, it must also be Bayesian.
- 2.
The choice of the right features is not a trivial matter.
- 3.
The principle gives the preference for global accommodation in terms of Heim (1983) and Van der Sandt (1992) in terms of BNLSP: nothing else would do. It gives however what I defend in Zeevat (1992), a preference for multiple accommodation, something which does not make sense on the versions of the satisfaction theory in these two references.
- 4.
Garcia Odon (2012) is an admirable discussion of the empirical facts around projection in Karttunian filters. Her analysis however rests on conditional perfection. Causal inferences seem a much better way of deriving the crucial pattern: \(p \rightarrow q\), where p is the presupposition and q the non-entailed cause of p. If it is given that p and that q is the cause of p then q must be the case as well. The non-projection in (15d) also shows that the causal explanation also works outside Karttunian filters.
- 5.
There are other ways of formulating the inequality, e.g. in all rational \(P\ P(x)< P(y)\). Rational probability assignments can be formalised straightforwardly on n-bounded models (“worlds”) for a finite first order language L. An n-bounded model has a domain with cardinality smaller than n. An n-bounded model can be seen—under isomorphism—as a row in a truth-table for propositional logic and can interpret a given set of connections by probabilities given directly by the frequencies for the connection in the model. This will assign a probability \(p_w(e)\) to an event e, deriving from the presence of other events in w and connections of them to e. Assume a probability distribution P over W, the set of worlds. P can be updated by bayesian update on the basis of observations e and the distributions \(p_w\) over events. The probability of a formula of L can now be equated with the sum of the probabilities of the worlds on which it is true. A rational probability assignment is an assignment P over W which respects the beliefs of the subject (the beliefs receive probability 1) and the experience of the subject, in the double sense that the experiences themselves are treated as beliefs and receive probability 1 and that the probability assignments to the worlds are updated by Bayes’ rule on the basis of those experiences. In this way, a world acquires more probability to the degree that its own frequencies predict the frequencies in the experience. The information state of the subject can be defined as the combination of the set of worlds it allows and the rational probability assignments over those worlds. Updates eliminate worlds and reassign probability by experience. It is possible to remove the restriction to n-bounded worlds, by using probability density functions and Bayesian updates over those, but that is not as straightforward.
- 6.
Bayesian nets are popular technology and introductions to Bayesian nets, their theory and their applications abound, as well as software environments for defining these nets and computing with them. Any attempt to give an example in these pages could not compete with what the reader can find immediately on the net. It is however unclear to the author how important Bayesian nets are for modeling the dynamic causal dependencies that are needed for BNLSP, though they definitely are an important source of inspiration.
- 7.
The probability of the effect given the possible cause should outweigh its probability if the possible cause did not obtain.
- 8.
Zeevat (2010) gives a more detailed discussion.
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Zeevat, H. (2015). Perspectives on Bayesian Natural Language Semantics and Pragmatics. In: Zeevat, H., Schmitz, HC. (eds) Bayesian Natural Language Semantics and Pragmatics. Language, Cognition, and Mind, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-17064-0_1
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