On 13 May 2014, Professor Gabriel Sandu visited Opole University and delivered the lecture entitled Quantifiers in natural language, independence friendly logic and its applications. Gabriel Sandu is a professor in the Department of Philosophy, History, Culture and Art Studies, University of Helsinki, Finland. The meeting with the Professor was organized jointly by the Group of Logic, Language and Information and the Institute of Philosophy of Opole University. It was held in the Plafond Hall in Collegium Maius of Opole University. The guest of the day arrived in Opole from Poznań, accompanied by Professor Andrzej Wiśniewski, the renowned logician, specialist in the field of logic of questions and semantics of natural language. At the beginning Professor Urszula Wybraniec-Skardowska welcomed the guests and the participants of the meeting. Then, Professor Janusz Czelakowski presented the scientific profile of the speaker.
One of the propositions concerning semantics of natural language, which has actively been developed in recent years, is framing it in terms of game theory. This current was commenced some years ago by works of Ehrenfeucht, which dealt with a game theoretical semantics for first order languages. The general and existential quantifiers are treated there as agents (players) called Abelard and Eloise or ∀dam and ∃va, respectively. The introduction of branching quantifiers by Henkin, as well as other types of quantifiers having their reference to natural language was of particular importance. The approach based on the game theory was grounded in works of Hintikka, and in contemporary times is widely applied in intensional logics, especially in epistemic logic. Professor Sandu is a disciple of Professor Hintikka and for many years has been carrying out research that propagates methods of the game theory in the scope of semantics of natural language, and also in foundations of logic and mathematics.
In his lecture, Professor Sandu made a review of applications of semantic methods based on the game theory with reference to natural language, foundations of mathematics and logic, with the inclusion of the latest achievements linking the game theory to probability. Independence friendly logic (IF logic) is an extension of first-order logic. In the formalized form it is designated as IFL. It takes into account dependences (or the lack of them) occurring between quantifiers, with the provision that the quantifiers run solely over individuals and not their sets. It is underlined that the relations of dependence or independence between the quantifiers are the sole tool to express the dependences or independences between individual variables. (For instance, old mathematical texts used the terms independent variable and dependent variable.) In natural languages, an example of the sentence where a quantifying dependence appears is the following one: I know who everybody admires. The possibility of providing in terms of IFL a compositional analysis of the de re / de dicto ambiguity in natural languages is also considered. It is well-known that on the semantic ground IFL is equivalent to existential second-order logic. IFL has other metaproperties in comparison with first-order logic. The appearance of IFL gave rise to philosophical discussions relating to the basic logical questions (the role of truth in axiomatic set theory), restructuring of logistic program, meaning of negation). In turn, the game-theoretical semantics of quantifiers (GTS) allows representing the relation of (in)dependence between variables in the terms of information (in)dependence, in the same way as the game theory frames it.
The above comments made the introduction to the exceptionally interesting lecture delivered by Professor Sandu, after which a discussion followed, touching on many themes with reference to the main theses of the lecture.