scholarly journals A logic of hypothetical conjunction

2019 ◽  
Vol 29 (6) ◽  
pp. 975-1009
Author(s):  
Matthew Collinson
Keyword(s):  
Computer Science ◽  
Possible Worlds ◽  
Conditional Logic ◽  
Binary Relations ◽  
Ternary Relation ◽  
Relevant Logics ◽  
Resource Reasoning ◽  
State Of Affairs ◽  
Natural Way

Abstract A binary connective that can be read as a matching conjunction for conditional connectives found in many conditional logics is considered. The most natural way to read this connective is often as a conjunction and yet, hypothetically, considered to hold of a state of affairs that could be obtained under the hypothesis. The connective can be given an intensional semantics extending a standard semantics of conditional logic that uses propositionally indexed families of binary relations on possible worlds. This semantics is determined by an adjoint relationship between the operations supporting the semantics of the conditional and the new conjunction. The semantics of the hypothetical conjunction connective subsumes the semantics, supported by a ternary relation semantics, of the fusion connective that arises in connection with substructural and relevant logics, and therefore subsumes a number of other forms of conjunction. A number of applications of the hypothetical conjunction connective are discussed, including generalized forms of resource reasoning used in computer science applications.

Information and Computer Security

2011 ◽  
pp. 1-23
Author(s):  
Lech J. Janczewski ◽  
Andrew M. Colarik
Keyword(s):  
United States ◽  
Information Security ◽  
Computer Security ◽  
Computer Science ◽  
The United States ◽  
The State ◽  
Science Laboratory ◽  
Computing Systems ◽  
Current State ◽  
State Of Affairs

The current state of the information security domain in the United States and much of the rest of the industrialized world can best be characterized as overly optimistic. The protection of computing systems and telecommunication infrastructures from unauthorized usage, manipulation, and sabotage faces serious challenges to ensure ongoing serviceability. This is especially true when we consider our growing dependence on these infrastructures. The state of affairs regarding the security aspects of these systems is even worse. Peter G. Neumann of the Computer Science Laboratory at SRI International in Menlo Park, California states:

Constructing the Impossible

2021 ◽  
pp. 141-163
Author(s):  
Kit Fine
Keyword(s):  
Natural Language ◽  
Possible Worlds ◽  
Formal Languages ◽  
Impossible Worlds ◽  
Possible World ◽  
Limited Role ◽  
Wide Range ◽  
Degree Of Acceptance ◽  
Broad Role ◽  
Natural Way

Please keep the original abstract. A number of philosophers have flirted with the idea of impossible worlds and some have even become enamored of it. But it has not met with the same degree of acceptance as the more familiar idea of a possible world. Whereas possible worlds have played a broad role in specifying the semantics for natural language and for a wide range of formal languages, impossible worlds have had a much more limited role; and there has not even been general agreement as to how a reasonable theory of impossible worlds is to be developed or applied. This chapter provides a natural way of introducing impossible states into the framework of truthmaker semantics and shows how their introduction permits a number of useful applications.

Relevant Logics

2019 ◽  
pp. 125-140
Author(s):  
Francesco Berto ◽  
Mark Jago
Keyword(s):  
Alternative Interpretation ◽  
Impossible Worlds ◽  
Ternary Relation ◽  
Information Theoretic ◽  
Relevant Logics ◽  
Ways Of Thinking

Relevant logics aim to avoid the ‘paradoxes’ of the material and strict conditionals. Their most natural semantics, the Routley-Meyer semantics, is given in terms of impossible worlds. By placing certain further conditions on those worlds, we can obtain stronger relevant logics. One of the main philosophical issues surrounding the general approach concerns how to interpret the Routley-Meyer ternary relation on worlds and the Routley star. The information-theoretic interpretation has proved popular but, it is argued, it faces philosophical issues. An alternative interpretation takes its cue from ways of thinking about conditionality in general. The three options are considered, but issues are found with each of them. A final option is the truthmaker interpretation of relevant logics, which is promising but under-developed.

Probabilities over rich languages, testing and randomness

1982 ◽  
Vol 47 (3) ◽  
pp. 495-548 ◽  
Author(s):  
Haim Gaifman ◽  
Marc Snir
Keyword(s):  
Formal Language ◽  
Possible Worlds ◽  
Random Sequence ◽  
A Priori ◽  
Mathematical Structure ◽  
Mathematical Framework ◽  
The Family ◽  
Logical Connectives ◽  
State Of Affairs ◽  
General Abstract

The basic concept underlying probability theory and statistics is a function assigning numerical values (probabilities) to events. An “event” in this context is any conceivable state of affairs including the so-called “empty event”—an a priori impossible state. Informally, events are described in everyday language (e.g. “by playing this strategy I shall win $1000 before going broke”). But in the current mathematical framework (first proposed by Kolmogoroff [Ko 1]) they are identified with subsets of some all-inclusive set Q. The family of all events constitutes a field, or σ-field, and the logical connectives ‘and’, ‘or’ and ‘not’ are translated into the set-theoretical operations of intersection, union and complementation. The points of Q can be regarded as possible worlds and an event as the set of all worlds in which it takes place. The concept of a field of sets is wide enough to accommodate all cases and to allow for a general abstract foundation of the theory. On the other hand it does not reflect distinctions that arise out of the linguistic structure which goes into the description of our events. Since events are always described in some language they can be indentified with the sentences that describe them and the probability function can be regarded as an assignment of values to sentences. The extensive accumulated knowledge concerning formal languages makes such a project feasible. The study of probability functions defined over the sentences of a rich enough formal language yields interesting insights in more than one direction.Our present approach is not an alternative to the accepted Kolmogoroff axiomatics. In fact, given some formal language L, we can consider a rich enough set, say Q, of models for L (called also in this work “worlds”) and we can associate with every sentence the set of all worlds in Q in which the sentence is true. Thus our probabilities can be considered also as measures over some field of sets. But the introduction of the language adds mathematical structure and makes for distinctions expressing basic intuitions that cannot be otherwise expressed. As an example we mention here the concept of a random sequence or, more generally, a random world, or a world which is typical to a certain probability distribution.

scholarly journals Sequential linked data: The state of affairs

Semantic Web ◽  
2021 ◽  
pp. 1-36
Author(s):  
Enrico Daga ◽  
Albert Meroño-Peñuela ◽  
Enrico Motta
Keyword(s):  
Semantic Web ◽  
Computer Science ◽  
Data Structures ◽  
Linked Data ◽  
Data Models ◽  
The State ◽  
Sequential Data ◽  
Linked List ◽  
Knowledge Graphs ◽  
State Of Affairs

Sequences are among the most important data structures in computer science. In the Semantic Web, however, little attention has been given to Sequential Linked Data. In previous work, we have discussed the data models that Knowledge Graphs commonly use for representing sequences and showed how these models have an impact on query performance and that this impact is invariant to triplestore implementations. However, the specific list operations that the management of Sequential Linked Data requires beyond the simple retrieval of an entire list or a range of its elements – e.g. to add or remove elements from a list –, and their impact in the various list data models, remain unclear. Covering this knowledge gap would be a significant step towards the realization of a Semantic Web list Application Programming Interface (API) that standardizes list manipulation and generalizes beyond specific data models. In order to address these challenges towards the realization of such an API, we build on our previous work in understanding the effects of various sequential data models for Knowledge Graphs, extending our benchmark and proposing a set of read-write Semantic Web list operations in SPARQL, with insert, update and delete support. To do so, we identify five classic list-based computer science sequential data structures (linked list, double linked list, stack, queue, and array), from which we derive nine atomic read-write operations for Semantic Web lists. We propose a SPARQL implementation of these operations with five typical RDF data models and compare their performance by executing them against six increasing dataset sizes and four different triplestores. In light of our results, we discuss the feasibility of our devised API and reflect on the state of affairs of Sequential Linked Data.

scholarly journals Arithmetic Formulated Relevantly

2021 ◽  
Vol 18 (5) ◽  
pp. 154-288
Author(s):  
Robert Meyer
Keyword(s):  
Intuitionistic Logic ◽  
Natural Deduction ◽  
Relevant Logic ◽  
Peano Arithmetic ◽  
Critical Problem ◽  
First Order ◽  
Order Form ◽  
Relevant Implication ◽  
Relevant Logics ◽  
Natural Way

The purpose of this paper is to formulate first-order Peano arithmetic within the resources of relevant logic, and to demonstrate certain properties of the system thus formulated. Striking among these properties are the facts that (1) it is trivial that relevant arithmetic is absolutely consistent, but (2) classical first-order Peano arithmetic is straightforwardly contained in relevant arithmetic. Under (1), I shall show in particular that 0 = 1 is a non-theorem of relevant arithmetic; this, of course, is exactly the formula whose unprovability was sought in the Hilbert program for proving arithmetic consistent. Under (2), I shall exhibit the requisite translation, drawing some Goedelian conclusions therefrom. Left open, however, is the critical problem whether Ackermann’s rule γ is admissible for theories of relevant arithmetic. The particular system of relevant Peano arithmetic featured in this paper shall be called R♯. Its logical base shall be the system R of relevant implication, taken in its first-order form RQ. Among other Peano arithmetics we shall consider here in particular the systems C♯, J♯, and RM3♯; these are based respectively on the classical logic C, the intuitionistic logic J, and the Sobocinski-Dunn semi-relevant logic RM3. And another feature of the paper will be the presentation of a system of natural deduction for R♯, along lines valid for first-order relevant theories in general. This formulation of R♯ makes it possible to construct relevantly valid arithmetical deductions in an easy and natural way; it is based on, but is in some respects more convenient than, the natural deduction formulations for relevant logics developed by Anderson and Belnap in Entailment.

scholarly journals A Second Opinion on the Current State of Affairs in Computer Science Education: An Australian Perspective

10.28945/2959 ◽  
2006 ◽  
Author(s):  
Lakshmi Narasimhan
Keyword(s):  
Science Education ◽  
Computer Science ◽  
Statistical Data ◽  
Computer Science Education ◽  
Trial And Error ◽  
Anglo Saxon ◽  
The Past ◽  
Current State ◽  
Student Enrolment ◽  
State Of Affairs

This paper presents a critical look at the likely demise of Computer Science (CS) as a discipline, in the light of various mishaps that academics in Universities have met with due to trial and error. We trace the issues of the past and present and, identify the reasons why computer science as a discipline in many Universities has not moved with time - in particular why it is not kept up with the pace required by the field. The loss of computer science is also well-reflected in the huge downturn in CS student enrolment across the Anglo-Saxon world. The paper also details some steps on how to change the ways and means of CS academics. We record that some of the arguments and recommendations presented in this paper can be controversial and may not necessarily relate to scenarios that exist in other countries. Further, some of the assertions made are without comprehensive statistical data, as we could not gather them, besides gathering anecdotal evidences.

CONCURRENT AUTOMATA AND DOMAINS

1992 ◽  
Vol 03 (04) ◽  
pp. 389-418 ◽  
Author(s):  
MANFRED DROSTE
Keyword(s):  
Concurrent Systems ◽  
Equivalence Classes ◽  
Binary Relations ◽  
Transition Systems ◽  
Operational Model ◽  
Locally Finite ◽  
Natural Domain ◽  
Theoretic Characterization ◽  
Natural Way

We introduce an operational model of concurrent systems, called automata with concurrency relations. These are labeled transition systems [Formula: see text] in which the event set is endowed with a collection of symmetric binary relations which describe when two events at a particular state of [Formula: see text] commute. This model generalizes the recent concept of Stark’s trace automata. A permutation equivalence for computation sequences of [Formula: see text] arises canonically, and we obtain a natural domain [Formula: see text] comprising the induced equivalence classes. We give a complete order-theoretic characterization of all such partial orders [Formula: see text] which turn out to be particular finitary domains. The arising domains [Formula: see text] are particularly pleasant Scott-domains, if [Formula: see text] is assumed to be concurrent, i.e. if the concurrency relations of [Formula: see text] depend (in a natural way) locally on each other, but not necessarily globally. We show that both event domains and dI-domains arise, up to isomorphism, as domains [Formula: see text] with well-behaved such concurrent automata [Formula: see text]. We introduce a subautomaton relationship for concurrent automata and show that, given two concurrency domains (D, ≤), (D′, ≤), there exists a nice stable embedding-projection pair from D to D′ iff D, D′ can be generated by concurrent automata [Formula: see text] such that [Formula: see text] is a subautomaton of [Formula: see text]. Finally, we introduce the concept of locally finite concurrent automata as a limit of finite concurrent automata and show that there exists a universal homogeneous locally finite concurrent automaton, which is unique up to isomorphism.

scholarly journals Explainable Certain Answers

2018 ◽  
Author(s):  
Giovanni Amendola ◽  
Leonid Libkin
Keyword(s):  
Incomplete Data ◽  
General Framework ◽  
Relational Databases ◽  
Possible Worlds ◽  
The Other ◽  
Closed World ◽  
Common Intersection ◽  
The Common ◽  
Certain Answers ◽  
Natural Way

When a dataset is not fully specified and can represent many possible worlds, one commonly answers queries by computing certain answers to them. A natural way of defining certainty is to say that an answer is certain if it is consistent with query answers in all possible worlds, and is furthermore the most informative answer with this property. However, the existence and complexity of such answers is not yet well understood even for relational databases. Thus in applications one tends to use different notions, essentially the intersection of query answers in possible worlds. However, justification of such notions has long been questioned. This leads to two problems: are certain answers based on informativeness feasible in applications? and can a clean justification be provided for intersection-based notions? Our goal is to answer both. For the former, we show that such answers may not exist, or be very large, even in simple cases of querying incomplete data. For the latter, we add the concept of explanations to the notion of informativeness: it shows not only that one object is more informative than the other, but also says why this is so. This leads to a modified notion of certainty: explainable certain answers. We present a general framework for reasoning about them, and show that for open and closed world relational databases, they are precisely the common intersection-based notions of certainty.

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