Abstract
Three-valued logics are standardly used to formalize gappy languages, i.e., interpreted languages in which sentences can be true, false or neither. A three-valued logic that assigns the same truth value to all gappy sentences is, in our view, insufficient to capture important semantic differences between them. In this paper we will argue that there are two different kinds of pathologies that should be treated separately and we defend the usefulness of a four-valued logic to represent adequately these two types of gappy sentences. Our purpose is to begin the formal exploration of the four-valued logics that could be used to represent the phenomena in question and to show that these phenomena are present in natural language, at least according to some semantic theories of natural language.
Acknowledgment
A version of this paper was presented at the IX Conference of the Spanish Society for Logic, Methodology and Philosophy of Science, held in Madrid in 2018, and at the Workshop on non-classical validity and logical pluralism, held in Barcelona in January 2020. We thank the audiences in both events for their comments. We wish to thank also an anonymous referee for this journal, for helpful comments and suggestions.
Research funding: The research for this paper has been funded by project 2019PID-107667GB-I00 of the Spanish Ministry of Science and Innovation and the European Union.
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