Maria Antonia Huertas

Universitat Oberta de Catalunya | UOC · Computer, Multimedia and Telecommunication Studies

Intensional Logic as understood here is a research program based upon the broad presupposition that so-called “intensional contexts” in natural language can be explained semantically by the idea of multiple reference.The inspiration for the semantic theories to be developed in this project is diverse, coming from linguistics, traditional philosophy, philosophical logic, philosophy of science, but also from computer science and mathematical logic. There is a difference between what a term designates and what it means. To go back to the paradigmatic example with which we started, “the morning star” and “the evening star” both designate the planet Venus, but they don't have the same meaning. The meaning of a term in a formal representation system is a proposition or declarative sentence and the denotation of a term is the object in the represented domain. Meanings, in this sense, are often called intensions, and things designated, extensions. Logics in which extension is all that matters are, naturally, called extensional, while logics in which extension is not enough are called intensional. Thus, temporal contexts require shifting patterns of ordinary Tarski-style denotations through time, modal contexts are related to varying denotations in some set of relevant worlds, or situations. Intensional logic attempts to study both designation and meaning and investigate the complex relationships between them. A number of versions of first order intensional logic can be found in the literature. They all face the following fundamental challenges: 1. Extensionalist tendencies in quantification and 2. De re and de dicto classical ambiguity 3. Troubles with identity 4. The need to introduce logical elements for tracing individuals across worlds/cases/times. This has led to complex formal systems or to systems incorporating extralogical/metaphysical notions, which are often useless for applications or fail to provide useful formal expressiveness. The systems also pay a price in that often they do not fully live up to standards of ease of use and uniformity. To address it, the proposed research focus is the formal representation of the intensional aspect, which, in a broad sense, may involves logic in philosophy, but also logic in other areas such as computer science, temporal knowledge representation and reasoning. Hybrid logic comes in because it has a long and impressive track record of “repairing” problems in modal and temporal logic in a simple and general way. The recent publication " Completeness in Hybrid Type Theory " (Areces, Blackburn, Huertas & Manzano (2013)) has demonstrated that hybrid logic is also capable of “repairing” problems involving logical completeness even in the setting of higher-order logic/type theory. Roughly speaking, it achieves this because it contains simple mechanisms for tracing an individual across worlds and times, and has a simple mechanism (the so-called downarrow binder) that is more powerful than predicate abstraction. Hybrid logic thus seems to open the door to a wide range of fundamental investigations in intensional logic and its applications, and the aim of this project is carry out these investigations in detail. More precisely, our goal is to investigate how far the combination of type theoretic machinery with hybrid logic can solve historical and contemporary problems (both philosophical and technical) in intensional logic, and to try and solve them in a simple, general, easy-to-use, framework