Papers by Dariusz Surowik
Studies in Logic, Grammar and Rhetoric, 2010
The aim of this paper is to discuss the following issue: what is rational behaviour of a lawyer (... more The aim of this paper is to discuss the following issue: what is rational behaviour of a lawyer (mainly in the process of the interpretation of legal texts)? We are especially interested if the 'is-ought problem' affects the issue.
The aim of this paper is to discuss the following issue: what is rational behaviour of a lawyer (... more The aim of this paper is to discuss the following issue: what is rational behaviour of a lawyer (mainly in the process of the interpretation of legal texts)? We are especially interested if the 'is-ought problem' affects the issue.
In this paper we describe the system of intuitionistic tense logic and consider the possibility o... more In this paper we describe the system of intuitionistic tense logic and consider the possibility of using this system to represent the changing of knowledge over time.
Summary. Some properties of finite groups are proved. The notion of cyclic group is defined next,... more Summary. Some properties of finite groups are proved. The notion of cyclic group is defined next, some cyclic groups are given, for example the group of integers with addition operations. Chosen properties of cyclic groups are proved next.
In recent years, temporal reasoning and knowledge representation is getting more attention. Tempo... more In recent years, temporal reasoning and knowledge representation is getting more attention. Temporal information is essential to most applications. The necessity for studying temporal reasoning and representing temporal knowledge arises in a wide range of disciplines including in particular philosophy, psychology or linguistics. Time and knowledge are strongly related. To formalize considerations about time we use a temporal logic and to formalize considerations about knowledge we use an epistemic logic. It seems obvious that to formalize considerations on knowledge changing in time, should be used some hybrid system. In this paper we will discuss some system of temporal epistemic logic and
The paper aims at providing temporal epistemic logic TEL with sound and complete axiomatization. ... more The paper aims at providing temporal epistemic logic TEL with sound and complete axiomatization. This logic combines temporal and epistemic operators. Time is represented as isomorphic to the set of natural numbers, whereas knowledge is modeled as an S5-like modality.
Certain elements of the mathematical theory of decision were developed as early as at the end of ... more Certain elements of the mathematical theory of decision were developed as early as at the end of the 19 century, or even earlier. The theory of probability and its applications to gambling were also highly developed. The concept of maximization of expected utility had already been introduced, however, it was not used for a long time. Still, the mature mathematical form of the theory of decision has been developed only recently. In the 1940s and 1950s a few works were published influencing greatly the development of mathematical research connected with the theory of decision, including The Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern (the theory of games) and The Foundations of Statistics by Leonard Savage (axiomatic foundations of the theory of subjective expected utility). These works formed the axiomatic bases for the contemporary theory of decision, and the results logically expanded in a number of theoretical findings from the beginning of the...
This paper discusses various conceptions of query languages for database systems (object oriented... more This paper discusses various conceptions of query languages for database systems (object oriented), in which objects are lists, trees and directed acyclic graphs. I use temporal logic as a modelling tool for the query languages under consideration. In the case of query language regarding lists, I will discuss temporal logic constituting an extension of linear time temporal logic, whereas in the case of query language regarding trees and directed acyclic graphs, I will discuss temporal logics constituting extensions of the branching–time temporal logic, the so called computation tree logic (CTL).
Summary. Some theorems and properties of cyclic groups have been proved with special regard to is... more Summary. Some theorems and properties of cyclic groups have been proved with special regard to isomorphisms of these groups. Among other things it has been proved that an arbitrary cyclic group is isomorphic with groups of integers with addition or group of integers with addition modulo m. Moreover, it has been proved that two arbitrary cyclic groups of the same order are isomorphic and that the class of cyclic groups is closed in consideration of homomorphism images. Some other properties of groups of this type have been proved too.
Logical determinism1 is a point of view which proves the thesis that only logical principles are ... more Logical determinism1 is a point of view which proves the thesis that only logical principles are sufficient while discussing determinism. Logical determinists say that the principles of bivalency and excluded middle low are sufficient to construct an argument about determinism. The problem was clearly formulated by Aristotle in Chapter IX of On Interpretation. Aristotle assumes that sentences about the past and present are either true or false. He claims, however, that the assumption that sentences about the future are either true or false is sufficient while constructing an argument about determinism. As he puts it:
In the information society, there exists an irresistible need, one may even say a necessity, to a... more In the information society, there exists an irresistible need, one may even say a necessity, to acquire and comprehend knowledge. Equipped with a sufficient level of knowledge and defined rules of inference, we are able to undertake specific decisions. In order to attain better representation and exploration of the ever expanding knowledge resources and to undertake appropriate decisions, we create constantly improved means of representing knowledge and enhanced methods of modelling situations for the real world. The language of classical logic is an appropriate tool for the formal description of statistical incidents. Incidents taking place in time require a novel approach. The power of expression, enabling a formal description of the time component, is made possible by the language of temporal logic. When we ask: What order should the complete information contained in a sentence have? the answer is simple. The information should have such form as to obtain answers to the questions...
A mathematical n-players game model can be represented in a normal or extensive form. A normal fo... more A mathematical n-players game model can be represented in a normal or extensive form. A normal form representation of games is ideal to represent situations where players make one choice and move simultaneously. An extensive form provides an explicit description of a strategic interaction by specifying a physical order of play, actions available to players each time they get to choose, and eventual payoffs for each player for any sequence of choices. For these reasons the extensive form provides a richer environment to study interesting questions such as rivalry, repeated interaction, etc. Obviously every normal form of the game can be represented in an extensive form, but it is more natural and simpler just to write the normal form. It is less obvious that every extensive form of the game can be written in a normal form. This translation is possible if we note that a strategy in an extensive form game is not just a move or sequence of moves, but rather is a complete contingency pla...
In the 1930’s mathematicians began to think about: What it means to be able to compute a function... more In the 1930’s mathematicians began to think about: What it means to be able to compute a function? It was the time, when a computability theory started. We may ask the next question: What is a computation? A simple answer would be as follows: a computation involves the mapping of a set of numbers to another set of numbers. But computation involves more. Namely, computation involves the use of finite procedures or algorithms to generate number mappings. A computation model is an entity that is capable of carrying out computations. One famous example of a computation model is the Turing Machine.
There are several systems of intuitionistic tense logic [1],[2],[3]. In the talk we would like to... more There are several systems of intuitionistic tense logic [1],[2],[3]. In the talk we would like to consider one of them given in [1] and called of IKt.. This is a minimal system of intuitionistic tense logic (no conditions are imposed upon earlier-later relation). We will propose a new axiomatization for this system. Our set of axioms is smaller than the set of axioms proposed by Ewald, then the new axiomatization is simpler. We will prove our axiomatization of IKt is equivalent to the Ewald’s axiomatization.
This paper discusses various conceptions of query languages for databasesystems(objectoriented),i... more This paper discusses various conceptions of query languages for databasesystems(objectoriented),inwhichobjectsarelists,treesanddirected acyclicgraphs.Iusetemporallogic asamodellingtool forthequerylanguages underconsideration.Inthecaseofquerylanguageregardinglists,Iwilldiscuss temporal logic constitutingan extensionof linear time temporal logic, whereas inthecaseofquerylanguage regardingtreesanddirectedacyclicgraphs,Iwill discusstemporal logics constitutingextensionsofthebranching-timetemporal logic, theso called computation tree logic (CTL).
Summary. Some properties of finite groups are proved. The notion of cyclic group is defined next,... more Summary. Some properties of finite groups are proved. The notion of cyclic group is defined next, some cyclic groups are given, for example the group of integers with addition operations. Chosen properties of cyclic groups are proved next.
Studies in Logic, Grammar and Rhetoric, 2009
Uploads
Papers by Dariusz Surowik