Abstract
We present a formalization of the Löbner-Barsalou frame theory (LBFT) in Dependence Logic with explicit strategies. In its present formalization, [Pet07], frames are defined as a particular kind of typed feature structures. On this approach, the semantic value of a lexical item is reduced to its contribution to the truth conditions of sentences in which it occurs. This reduction does neither account for dynamic phenomena nor for results from neuroscience which show that meaning cannot be reduced to truth conditions. In order to overcome these shortcomings, we develop a dynamic frame theory which is based both on Dependence Logic [Vää07] and Dynamic Epistemic Logic ([vB11]). The semantic phenomenon with respect to which this framework is tested are numerical expressions like ‘two’ or ‘at least two’. They are interpreted as strategies which change the input information state to which they are applied.
The research was supported by the German Science Foundation (DFG) funding the Collaborative Research Center 991.
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Notes
- 1.
Of course, this need in general not to be true for arbitrary observations. Here we refer to the circumstances under which the children and the adults observed the scene where three horses jumped over a fence.
- 2.
Though using his knowledge that bare numerals are often used with an ‘at least’ interpretation when used distributively, this may be the preferred assumption.
- 3.
This follows from the example in (12) as well as the examples from Musolino’s first two experiments.
- 4.
Note that single teams can express uncertainty too. This is the case whenever the values of an attribute form a filter or an ideal. However, this uncertainty is due to the interpretation of the expression and need not arise from epistemic uncertainty.
- 5.
Here, we implicitly assumed the initialization assumption which will be introduced in (25) in Sect. 4.4.
- 6.
This does not mean that the observation is specific in the sense that an attribute is assigned a unique value. For example, without counting the number of horses that one sees one can say that one is seeing at most / at least n horses.
- 7.
For details on the distinction between strict and lax semantics in Dependence Logic, see [Gal12].
- 8.
A more fine-grained update or supplement operation can be defined if one uses a sort hierarchy on the values of an attribute. Using such a hierarchy, the value of the type attribute in the above example would be calculated as the greatest lower bound of the values in the corresponding elements of the teams.
- 9.
The indices at horse are used for better readability. Actually, horse has to be used without indices because the value of the base attribute is a Link-sum object over the values of the type attribute.
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Naumann, R., Petersen, W. (2015). Frame Theory, Dependence Logic and Strategies. In: Aher, M., Hole, D., Jeřábek, E., Kupke, C. (eds) Logic, Language, and Computation. TbiLLC 2013. Lecture Notes in Computer Science(), vol 8984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46906-4_13
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