This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak systems there are at least two (...) approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. (shrink)

Piero della Francesca is best known as a painter but he was also a mathematician. His treatise De prospectiva pingendi is a superb example of a union between the fne arts and mathemati‑ cal sciences of arithmetic and geometry. In this paper, I explain some reasons why his paint‑ ing is considered as a part of perspective and, therefore, can be identifed with a branch of geometry.

Artykuł ten powstał w wyniku realizacji projektu badawczego nr 2012/07/B/HS1/01986.

This paper introduces and studies a declarative framework for updating views over indefinite databases. An indefinite database is a database with null values that are represented, following the standard database approach, by a single null constant. Typically a database is represented by a single set of facts |$D$| that model what is known to be true. This paper proposes a model of an indefinite extensional database that is more expressive with respect to the closed-world assumption (CWA) adapted for the setting (...) of indefinite databases (Libkin, 1995, A semantics-based approach to design of query languages for partial information. In Semantics in Databases, vol. 1358 of LNCS, pp. 170–208. Springer; der Meyden, 1998, Logical approaches to incomplete information: a survey. In Logics for Databases and Information Systems, pp. 307–356. Kluwer Academic Publishers, Norwell, MA, USA). More specifically, in our model, databases are determined by two sets of facts: |$D$| representing, as usual, all facts that are true in the database, and |$E$| that is meant to represent exceptions to the ‘unknown range’, i.e. facts that cannot be unknown. Intuitively, unless they are explicitly implied to be true by the first set, the facts specified as exceptions are assumed false. The semantics is given by means of a two-level CWA tailored to the case of indefinite information. The paper characterizes the semantics of indefinite databases in terms of their possible worlds that are obtained by instantiating occurrences of null values by concrete constants and defines several classes of database repairs that realize view-update requests. Most notable is the class of constrained repairs. Constrained repairs change the database ‘minimally’and avoid making arbitrary commitments. They narrow down the space of alternative ways to fulfill the view-update request to those that are grounded, in a certain strong sense, in the database, the view and the view-update request. (shrink)

We show that modal logics characterized by a class of frames satisfying the insertion property are suitable for Reiter's default logic. We refine the canonical fix point construction defined by Marek, Schwarz and Truszczyński for Reiter's default logic and thus we addrress a new paradigm for nonmonotonic logic. In fact, differently from the construction defined by these authors. we show that suitable modal logics for such a construction must indeed contain K D4. When reflexivity is added to the modal logic (...) used for the fix point construction then we come to the Marek Schwarz and Truszczyński framework for Reiter's default logic. Our framework, in fact, is appropriate also to the family of modal logics in between S4 and S4f. If, instead, reflexivity is dropped, then we show that a new family of modal logics is gained, namely the modal logics in between KD4 and KD4Z. The upper bound can be extended to the modal logic KD4LZ whenever the propositional language taken into account is finite. (shrink)