In semantics one attempts to give a systematic account of the meaning of sentences in natural language. This is everything but a trivial affaire. In particular, so-called self-referential sentences offer a stumbling block for developing natural language semantics but have been largely ignored by semanticists. However, research on self-reference and self-referential sentences is abundant in philosophy and philosophical logic in form of research on the Liar paradox (This sentence is not true. True or False?) and related paradoxes. Indeed, a number of accounts for dealing with self-reference have been developed in those fields---mostly in the form of theories of truth that avoid the paradoxical consequences. Implementing theories of truth within the framework of natural language semantics therefor amounts to an important step towards a satisfactory handling of self-referential sentences within natural language semantics.
This implementation runs into major problems with respect to, e.g. the semantics for natural language conditionals, various quantifiers, belief ascriptions and, more generally so-called hyperintensional semantics. One principal focus of the research project was to develop theories of truth for these different semantics and thereby provide the groundwork for satisfactory semantics of such contexts in the presence of self-referential, liar-like sentences. A second principal focus of the project is to assume a more metasemantic perspective and reflect on the foundations of natural language semantics conceived of as truth-conditional semantics. This raises the question of whether the natural language truth predicate (‘is true’) is related to the truth predicate employed in semantics, and if so how? Answering this question is again non-trivial and requires a thorough linguistic analysis of the natural language truth predicate, an investigation of the technical prospects and limitations of a semantic framework encapsulating this idea, as well as a comparison to views that conceives of the semantic truth predicate as a merely theoretical notion.
Overall, the project can be deemed a success. In particular, with respect to the first focal point a rich toolkit for constructing natural language semantics that can adequately process various forms of self-reference. As for the second focal point, the research is arguably more open-ended. Nonetheless the project has delivered progress of our understanding of the natural language truth predicate, the properties of truth that can be consistently assumed in a formally regimented context, as well as a foray into semantics that are self-applicable and thus allow for an identification of the semantic and natural language, i.e. object-linguistic truth predicate.
The research is of a highly abstract and foundational nature, so pointing toward any immediate importance for society, which goes beyond the scientific importance of the project for understanding key philosophical notions such as truth and belief, natural language semantics, and self-reference, is a difficult task. However, handling self-reference is also one of the major challenges and stumbling blocks of the research on artificial intelligence and, albeit in a very indirect way, our research may raise awareness and improve our understanding of the challenges to come.
