Creativeness and completeness in recursion categories of partial recursive operators

1989 ◽  
Vol 54 (3) ◽  
pp. 1023-1041 ◽  
Author(s):  
Franco Montagna ◽  
Andrea Sorbi
Keyword(s):  
Classical Result ◽  
Basic Result ◽  
Recursion Theory ◽  
Theoretic Approach ◽  
Classical Notion ◽  
Algebraic Treatment ◽  
Recursive Operators ◽  
The Way

Recursion categories have been proposed by Di Paola and Heller in [DPH] as the basis for a category-theoretic approach to recursion theory, in the context of a more general and ambitious project of a purely algebraic treatment of incompleteness phenomena. The way in which the classical notion of creative set is rendered in this new category-theoretic framework plays, therefore, a central role. This is done in [DPH] (Definition 8.1) by defining the notion of creative domains or, rather, domains which are creative relative to some criterion: thus, in a recursion category, every criterion provides a notion of creativeness.A basic result on creative domains (cf. [DPH, Theorem 8.13]) is that, under certain assumptions, a version of the classical result, due to Myhill [MYH], stating that every creative set is complete, holds: in a recursion category with equality (i.e. exists for every object X) and having enough atoms, every domain which is creative with respect to atoms is also complete.

Advances in Digital Forensics Frameworks and Tools

2018 ◽  
Vol 10 (2) ◽  
pp. 95-119
Author(s):  
Muhammad Abulaish ◽  
Nur Al Hasan Haldar
Keyword(s):  
Digital Media ◽  
Digital Forensics ◽  
Process Models ◽  
Computer Assisted ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Comparative Survey ◽  
Definition Of ◽  
The Way

Digital forensics science is a well-known initiative to unearth computer-assisted crimes. The thriving criminal activities using digital media have changed the typical definition of a traditional crime. Meanwhile, the means and targets of criminal activities have been transformed in a broader context due to the diverse nature of offenses associated with the multiple crime categories, affecting the way of investigations as well. In order to withstand the difficulties caused due to the crime complexity, forensics investigation frameworks are being tuned to adjust with the nature and earnestness of the felonies being committed. This article presents an in-depth comparative survey of fourteen popular and most cited digital forensics process models and various forensics tools associated with different phases of these models. The relationships among these forensics process models and their evolutions are analyzed and a graph-theoretic approach is presented to rank the existing process models to facilitate investigators in selecting an appropriate model for their investigation tasks.

Advances in Digital Forensics Frameworks and Tools

2020 ◽  
pp. 165-191
Author(s):  
Muhammad Abulaish ◽  
Nur Al Hasan Haldar
Keyword(s):  
Digital Media ◽  
Digital Forensics ◽  
Process Models ◽  
Computer Assisted ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Comparative Survey ◽  
Definition Of ◽  
The Way

Digital forensics science is a well-known initiative to unearth computer-assisted crimes. The thriving criminal activities using digital media have changed the typical definition of a traditional crime. Meanwhile, the means and targets of criminal activities have been transformed in a broader context due to the diverse nature of offenses associated with the multiple crime categories, affecting the way of investigations as well. In order to withstand the difficulties caused due to the crime complexity, forensics investigation frameworks are being tuned to adjust with the nature and earnestness of the felonies being committed. This article presents an in-depth comparative survey of fourteen popular and most cited digital forensics process models and various forensics tools associated with different phases of these models. The relationships among these forensics process models and their evolutions are analyzed and a graph-theoretic approach is presented to rank the existing process models to facilitate investigators in selecting an appropriate model for their investigation tasks.

Philosophical connections between the classical and the modern notion of corruption

2017 ◽  
Vol 24 (1) ◽  
pp. 82-100
Author(s):  
Michel Dion
Keyword(s):  
Transition Period ◽  
Adam Smith ◽  
Reference Points ◽  
The Body ◽  
Future Research ◽  
Content Type ◽  
Conditioning Factors ◽  
Classical Notion ◽  
Historical Periods ◽  
The Way

Purpose The purpose of this paper is to circumscribe the various philosophical connections between the classical and the modern notion of corruption from Enlightenment to post-modernity. Design/methodology/approach The paper analyzed to what extent the classical notion of corruption (Plato, Aristotle and Cicero) still influenced the way philosophers perceived the phenomenon of corruption during the Enlightenment (1625-1832), the transition period (1833-1900) and the post-modernity (1901 onward). Taking those historical periods as reference points, the author will see how literature about historical, social and political conditioning factors of corruption could convey the presence/absence of the classical or the modern notion of corruption. Findings The paper finds that the classical notion of corruption implies the degeneration of human relationships (Plato and Hegel), the degeneration of the body-and-mind unity (Aristotle, Pascal and Thomas Mann) or the degeneration of collective morality (Cicero, Locke, Rousseau, Hume and Kant). The modern notion of corruption as bribery was mainly introduced by Adam Smith. Nietzsche (and Musil) looked at corruption as degeneration of the will-to-power. The classical notion of corruption put the emphasis on the effects rather than on the cause itself (effects-based thinking). The modern notion of corruption as bribery insists on the cause rather than on the effects (cause-based thinking). Research limitations/implications In this paper, the author has taken into account the main representatives of the three historical periods. Future research could also analyze the works of other philosophers and novelists to see to what extent their philosophical and literary works are unveiling the classical or the modern notion of corruption. Originality/value The paper presents a philosophical and historical perspective about corruption. It sheds light on the way philosophers (and sometimes novelists) deal with the issue of corruption, whether it is from an effects-based or from a cause-based perspective.

Intermediate β-r.e. degrees and the half-jump

1983 ◽  
Vol 48 (3) ◽  
pp. 790-796
Author(s):  
Steven Homer
Keyword(s):  
Recursion Theory ◽  
Density Theorem ◽  
The Way

In his thesis [2] Sy Friedman showed that for any inadmissible ordinal β there is an easily definable β-r.e. degree, 01/2, with β-degree strictly between 0 and 0′. In this paper we define, for some weakly admissible β, a β-r.e. degree 03/4 intermediate between 01/2 and 0′. This definition is given using the machinery developed by Maass [6], [7] to study the β-r.e. degrees.A weak jump for β-recursion theory, the ½-jump, was first defined by Friedman [4] and has been studied by Sacks and Homer [5]. The degree 03/4 is of interest because of the way it interacts with the half-jump. In particular 03/4 forms the boundary between the half-jump of “hyperregular” and “nonhyperregular” β-r.e. degrees less than 01/2. One consequence of these results is that there are weakly inadmissible β for which either the jump theorem or the density theorem fails.Much of this paper is based on earlier work in this area by Sy Friedman and Wolfgang Maass. I would like to thank Gerald Sacks for many helpful conversations and comments concerning this work.

Advances in Digital Forensics Frameworks and Tools

2020 ◽  
pp. 374-401
Author(s):  
Muhammad Abulaish ◽  
Nur Al Hasan Haldar
Keyword(s):  
Digital Media ◽  
Digital Forensics ◽  
Process Models ◽  
Computer Assisted ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Comparative Survey ◽  
Definition Of ◽  
The Way

Digital forensics science is a well-known initiative to unearth computer-assisted crimes. The thriving criminal activities using digital media have changed the typical definition of a traditional crime. Meanwhile, the means and targets of criminal activities have been transformed in a broader context due to the diverse nature of offenses associated with the multiple crime categories, affecting the way of investigations as well. In order to withstand the difficulties caused due to the crime complexity, forensics investigation frameworks are being tuned to adjust with the nature and earnestness of the felonies being committed. This article presents an in-depth comparative survey of fourteen popular and most cited digital forensics process models and various forensics tools associated with different phases of these models. The relationships among these forensics process models and their evolutions are analyzed and a graph-theoretic approach is presented to rank the existing process models to facilitate investigators in selecting an appropriate model for their investigation tasks.

Shepherdson Revisited

1993 ◽  
Author(s):  
Raymond M. Smullyan
Keyword(s):  
Recursive Function ◽  
Recursion Theory ◽  
First Order ◽  
The Way

Theorems A and B of the last chapter were proved using previous results about generativity, Kleene pairs, complete effective inseparability, and double generativity. Yet the two theorems made no mention of these notions; they referred only to the notions of universality, double universality and semi-double universality. [These three notions, by the way, unlike the four notions mentioned above, were denned without reference to any indexing; they are what we would call index-free.] Is it not possible to give more direct proofs of Theorems A and B that do not require all the antecedent machinery of Chapters 4 and 5? We are about to show that it is possible; we will simply transfer Shepherdson’s arguments about first-order systems to recursion theory itself. We shall prove some “recursive function-theoretic” analogues of Shepherdson’s theorems which will provide new proofs of Theorems A and B (in fact, a strengthening of Theorem A will result).

Users' Relevance on the Web

2010 ◽  
pp. 411-423 ◽  
Author(s):  
Francisco Yus
Keyword(s):  
Relevance Theory ◽  
Mental Effort ◽  
Point Of View ◽  
Web Pages ◽  
Theoretic Approach ◽  
Cognitive Effects ◽  
Web Page ◽  
Internet Users ◽  
The Web ◽  
The Way

In this chapter the author analyzes, from a cognitive pragmatics point of view and, more specifically, from a relevance-theoretic approach, the way Internet users assess the qualities of web pages in their search for optimally relevant interpretive outcomes. The relevance of a web page is measured as a balance between the interest that information provides (the so-called “positive cognitive effects” in relevance theory terminology) and the mental effort involved in their extraction. On paper, optimal relevance is achieved when the interest is high and the effort involved is low. However, as the relevance grid in this chapter shows, there are many possible combinations when measuring the relevance of content on web pages. The author also addresses how the quality and design of web pages may influence the way balances of interest (cognitive effects) and mental effort are assessed by users when processing the information contained on the web page. The analysis yields interesting implications on how web pages should be designed and on web usability in general.

Interpreting Davidson's Omniscient Interpreter

1995 ◽  
Vol 25 (3) ◽  
pp. 335-374 ◽  
Author(s):  
Richard N. Manning
Keyword(s):  
Basic Result ◽  
External World ◽  
Donald Davidson ◽  
Point Of View ◽  
Critical Response ◽  
External World Skepticism ◽  
Almost All ◽  
The Way

Donald Davidson infamously claims that belief is in its nature veridical, and that skepticism is for this reason fundamentally incoherent. To those who take the issue of external world skepticism seriously, Davidson's arguments may seem to involve a conjuring trick. In particular, his invocation of an ‘omniscient interpreter’, whose intelligibility supposedly ensures that our beliefs must be largely true, has the air of incense and lantern-rubbing about it. Davidson's claim has received considerable critical response in the literature, almost all of it negative. In my view, some commentators have indeed lit on a critical and controversial lemma in Davidson's argument, but this basic result has been obscured by being presented amidst an array of other criticisms that simply make no sense from a Davidsonian point of view. The aim of this paper is to clear away some of the confusion that stands in the way of a more productive evaluation of Davidson's important claim.

Well-behaved modal logics

1984 ◽  
Vol 49 (4) ◽  
pp. 1393-1402
Author(s):  
Harold T. Hodes
Keyword(s):  
Modal Logic ◽  
Model Theory ◽  
Classical Model ◽  
Classical Case ◽  
Recursion Theory ◽  
Modal Logics ◽  
Modal Model ◽  
The Right ◽  
Domain Property ◽  
The Way

Much of the literature on the model theory of modal logics suffers from two weaknesses. Firstly, there is a lack of generality; theorems are proved piecemeal about this or that modal logic, or at best small classes of logics. Much of the literature, e.g. [1], [2], and [3], confines attention to structures with the expanding domain property (i.e., if wRu then Ā(w) ⊆ Ā(u)); the syntactic counterpart of this restriction is assumption of the converse Barcan scheme, a move which offers (in Russell's phrase) “all the advantages of theft over honest toil”. Secondly, I think there has been a failure to hit on the best ways of extending classical model theoretic notions to modal contexts. This weakness makes the literature boring, since a large part of the interest of modal model theory resides in the way in which classical model theoretic notions extend, and in some cases divide, in the modal setting. (The relation between α-recursion theory and classical recursion theory is analogous to that between modal model theory and classical model theory. Much of the work in α-recursion theory involved finding the right definitions (e.g., of recursive-in) and separating concepts which collapse in the classical case (e.g. of finiteness and boundedness).)The notion of a well-behaved modal logic is introduced in §3 to make possible rather general results; of course our attention will not be restricted to structures with the expanding domain property. Rather than prove piecemeal that familiar modal logics are well-behaved, in §4 we shall consider a class of “special” modal logics, which obviously includes many familiar logics and which is included in the class of well-behaved modal logics.

Sign in / Sign up

Export Citation Format

Share Document