Logical structures and intentionality
Project Director dr. sc. Srećko Kovač
The project is devoted to several current research topics in logic, such as non-standard models in first order modal logic (e.g. Fitting, 2004, Ye and Fitting, 2002), dynamic semantics in practical logic (e.g. van Benthem and Liu 2005.), abstract model theory (e.g. Beziau, ed. 2005). The variety of logical structures for modeling agent’s intentional states will be developed, examined, and compared. Special attention will be paid to nonstandard models of cognitive and volitive states. The logics of intentional states will be compared within abstract model theory. 1) Cognitive intentional states (belief, knowledge, etc.) will be modelled using the tools of non-standard first-order modal logic, and an appropriate tableau system will be proposed. The basic questions to be solved are paraconsistency, identity of objects, mode of presentation of objects, intended fictive objects, paradoxes of belief, the relation between de dicto and de re epistemic sentences, temporal knowledge. One topic is also the way belief change is dependent on the inconsistency of agent’s beliefs. Temporal reasoning will be modelled by means of BDI (Belief Desire Intention) models. 2) Volitive intentional states will be analyzed using dynamic semantics. The relation of logic of volitive states with imperative and erotetic logic will be examined. The dynamic semantics for quantificational imperative logic will be constructed and a labelled natural deduction system will be developed. 3) The mode of presentation independent intentionality will be analyzed on the example of the “attributive” interpretation of Gödel’s ontological proof. 4) Abstract logic of intentionality will be examined. Also, the concept of logical structure in general and the structuralistic conception in philosophy of logic and mathematics will be investigated. The equivalence and identity of structures, as well as morphisms between logics will be examined on the basis of a general theory of logical structures. 5) Within the context of the history of Croatian philosophy and logic, the concepts of space and infinity will be analyzed in Meršić’s critique of Hilbert’s axiomatics and of the logic of infinity (1914).