Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

Results found: 8

first rewind previous Page / 1 next fast forward last

Search results

Search:
in the keywords:  decidability
help Sort By:

help Limit search:
first rewind previous Page / 1 next fast forward last
1

Propositions, Possible Worlds, and Recursion

100%
Wiśniewski A.
Logic and Logical Philosophy
|
2011
|
vol. 20
|
issue 1-2
73-79
EN
The issue of reduction of propositions to sets of possible worlds is addressed. It is shown that, under some natural assumptions, there always exist recursive propositions, i.e. decidable sets of possible worlds, which are not assigned to any sentence of a language. Some consequences of this result are discussed.
2

O rozstrzygalności teologii

88%
Olszewski A.
Teologia w Polsce
|
2020
|
vol. 14
|
issue 2
77-102
EN
The paper takes a synthetic, not an analytical approach to the title issue. From the methodological point of view, it is an attempt to apply logical notions such as consequence, proof, rule and decidability to theology as a whole. In the first part (to the paragraph 3.1) the theology is considered as a logical theory and the drawbacks of such an approach are pointed out, including the impossibility of a sensible consideration of the decidability of such a theology. The second part weakens the logical notion of decidability and narrows down the notion of theology for which the weakened decidability can be applied. The whole discussion poses a lot of problems concerning theology, which probably theologians should solve. The work is quite controversial for both sides: theologians and logicians. To make it easier for theologians to read the paper, a glossary of loosely worded terms of logical terms has been added.
3

More on The Decidability of Mereological Theories

88%
Tsai H.-c.
Logic and Logical Philosophy
|
2011
|
vol. 20
|
issue 3
251-265
EN
Quite a few results concerning the decidability of mereological theories have been given in my previous paper. But many mereological theories are still left unaccounted for. In this paper I will refine a general method for proving the undecidability of a theory and then by making use of it, I will show that most mereological theories that are strictly weaker than CEM are finitely inseparable and hence undecidable. The same results might be carried over to some extensions of those weak theories by adding the fusion axiom schema. Most of the proofs to be presented in this paper take finite lattices as the base models when applying the refined method. However, I shall also point out the limitation of this kind of reduction and make some observations and conjectures concerning the decidability of stronger mereological theories.
4
Content available remote

On Displaying Negative Modalities

75%
Drobyshevich S.
Logic and Logical Philosophy
|
2018
|
vol. 27
|
issue 2
161-192
XX
We extend Takuro Onishi’s result on displaying substructural negations by formulating display calculi for non-normal versions of impossibility and unnecessity operators, called regular and co-regular negations, respectively, by Dimiter Vakarelov. We make a number of connections between Onishi’s work and Vakarelov’s study of negation. We also prove a decidability result for our display calculus, which can be naturally extended to obtain decidability results for a large number of display calculi for logics with negative modal operators.
5

Special Issue on point-free geometry and topology. An introduction

63%
Coppola C., Gerla G.
Logic and Logical Philosophy
|
2013
|
vol. 22
|
issue 2
139-143
EN
In the first section we briefly describe the methodological assumptions of point-free geometry and topology. We also outline the history of geometrical theories based on the notion of a region. The second section is devoted to a concise presentation of the content of the LLP special issue on point-free theories of space.
6

Finitely Inseparable First-Order Axiomatized Mereotopological Theories

63%
Tsai H.-c.
Logic and Logical Philosophy
|
2013
|
vol. 22
|
issue 3
347-363
EN
This paper will first introduce first-order mereotopological ax- ioms and axiomatized theories which can be found in some recent litera- ture and it will also give a survey of decidability, undecidability as well as other relevant notions. Then the main result to be given in this paper will be the finite inseparability of any mereotopological theory up to atomic general mereotopology (AGEMT) or strong atomic general mereotopology (SAGEMT). Besides, a more comprehensive summary will also be given via making observations about other properties stronger than undecidability.
7
Publication available in full text mode
Content available

O rozstrzygalności teologii

63%
Olszewski A.
Teologia w Polsce
|
2020
|
vol. 14
|
issue 2
77-102
EN
The paper takes a synthetic, not an analytical approach to the title issue. From the methodological point of view, it is an attempt to apply logical notions such as consequence, proof, rule and decidability to theology as a whole. In the first part (to the paragraph 3.1) the theology is considered as a logical theory and the drawbacks of such an approach are pointed out, including the impossibility of a sensible consideration of the decidability of such a theology. The second part weakens the logical notion of decidability and narrows down the notion of theology for which the weakened decidability can be applied. The whole discussion poses a lot of problems concerning theology, which probably theologians should solve. The work is quite controversial for both sides: theologians andlogicians. To make it easier for theologians to read the paper, a glossary of loosely worded terms of logical terms has been added.
PL
W pracy przedstawiono syntetyczne, a nie analityczne, ujęcie tytułowego zagadnienia. Od strony metodologicznej jest próbą aplikacji pojęć logicznych jak konsekwencja, dowód, rozstrzygalność do teologii jako całości. W pierwszej części (do pkt 3.1) rozważa się teologię jako teorię logiczną i wskazuje na wady takiego ujęcia, w tym na niemożliwość sensownego rozważania rozstrzygalności tak rozumianej teologii. W drugiej części zostało osłabione logiczne pojęcie rozstrzygalności oraz zawężone pojęcie teologii, dla którego osłabiona rozstrzygalność daje się zastosować. W rozważaniach postawiono mnóstwo problemów dotyczących teologii, które chyba teologowie powinni rozwiązać. Praca jest dość kontrowersyjna dla obu stron, czyli teologów i logików. Aby ułatwić teologom lekturę pracy, dodano słowniczek luźno sformułowanych określeń terminów logicznych.
8
Publication available in full text mode
Content available

Does Science Progress Towards Ever Higher Solvability Through Feedbacks Between Insights and Routines?

45%
Marciszewski W.
Studia Semiotyczne
|
2018
|
vol. 32
|
issue 2
153-185
EN
The affirmative answer to the title question is justified in two ways: logical and empirical. (1) The logical justification is due to Gödel’s discovery (1931) that in any axiomatic formalized theory, having at least the expressive power of PA (Peano Arithmetic), at any stage of development there must appear unsolvable problems. However, some of them become solvable in a further development of the theory in question, owing to subsequent investigations. These lead to new concepts, expressed with additional axioms or rules. Owing to the so-amplified axiomatic basis, new routine procedures like algorithms, can be reached. Those, in turn, help to gain new insights which lead to still more powerful axioms, and consequently again to ampler algorithmic resources. Thus scientific progress proceeds to an ever higher scope of solvability. (2) The existence of such feedback cycles – in a formal way rendered with Turing’s systems of logic based on ordinal (1939) – gets empirically supported by the history of mathematics and other exact sciences. An instructive instance of such a process is found in the history of the number zero. Without that insight due to some ancient Hindu mathematicians there could not arise such an axiomatic theory as PA. It defines the algorithms of arithmetical operations, which in turn help intuitions; those, in turn, give rise to algorithmic routines, not available in any of the previous phases of the process in question. While the logical substantiation of the point of this essay is a well-established result of logico-semantic inquiries, its empirical claim, based on historical evidences, remains open for discussion. Hence the author’s intention to address philosophers and historians of science, and to encourage their critical responses.
first rewind previous Page / 1 next fast forward last
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.