Dependence Logic with Generalized Quantifiers: Axiomatizations

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as "there exists uncountable many." Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.Comment: 17 page

Dependencies Between Quantifiers Vs. Dependencies Between Variables

Peer reviewe

Dependence logic with generalized quantifiers : Axiomatizations

Peer reviewe

Presupozicije, logika i dinamika vjerovanja

In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the role of presupposition in supervaluations logical systems. At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notions.U istraživanju presupozicija u odnosu na logiku i dinamiku vjerovanja razlikujemo dva povezana dijela. Prvi dio se odnosi na presupozicije i logiku koja ne mora biti povezana s intenzionalnim operatorima. Tu se primarno koncentriramo na klasičnu, slobodnu i presupozicijsku logiku. U odnosu na klasičnu logiku razmatramo dobro poznati Strawsonov pristup problemu presupozicija. Nadalje, razmatramo slobodne logike, posebice van Fraassenovo istraživanje uloge presupozicija u supervaluacijskim logičkim sistemima. Na kraju prvog dijela razmatramo izvornu Thomasonovu izgradnju presupozicijske logike. Drugi dio se odnosi na povezanost presupozicija i logike dinamike vjerovanja. Ovdje razmatramo logiku promjene vjerovanja u okviru epistemičkih pojmova imanentnih mehanizmu dinamičke logike. Tri razmatrana pristupa su situacijska semantika (Barwise, Perry), teorija promjene vjerovanja, odnosno, Alchourron/Gärdenfors/Makinsonova (AGM) teorija, te na kraju Hintikkin pristup u izgradnji epistemièke logike

Presuppositions, Logic, and Dynamics of Belief

In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the role of presupposition in supervaluations logical systems. At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notion

Games and Logic

The idea behind these games is to obtain an alternative characterization of logical notions cherished by logicians such as truth in a model, or provability (in a formal system). We offer a quick survey of Hintikka\u27s evaluation games, which offer an alternative notion of truth in a model for first-order langauges. These are win-lose, extensive games of perfect information. We then consider a variation of these games, IF games, which are win-lose extensive games of imperfect information. Both games presuppose that the meaning of the basic vocabulary of the language is given. To give an account of the linguistic conventions which settle the meaning of the basic vocabulary, we consider signaling games, inspired by Lewis\u27 work. We close with IF probabilistic games, a strategic variant of IF games which combines semantical games with von Neumann\u27s minimax theorem