In this paper, the Multi-flow Asynchronous Temporal Logic, called MAT Logic, is presented. MAT Logic is a new temporal×modal logic with non-deterministic operators among time flows as accessibility relations. The main goal of this work has been the design and description of a logic that could be capable of managing communications among systems with not necessarily synchronizable time flows. In order to better understand the design of the logic, an example in the field of communications is given.

MAT logic: a temporal×modal logic with non-deterministic operators to deal with interactive systems in communication technologies

In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporal×modal logic. The main result is the proof of definability of these definitions which is obtained by using algebraic characterizations. As a consequence, we will have in our temporal×modal context the generalizations of modal logics T, S4, S5, KD45, etc. These new logics will allow us to establish connections among time flows in very different ways, which enables us to carry out different relations among asynchronous systems. Our further research is focused on the construction of logics with these properties and the design of theorem provers for these logics.

Generalization of some properties of relations in the context of functional temporal×modal logic

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them Different properties of the accessibility functions (being injective, surjective, increasing, etc) have been considered and axiomatic systems (called functional) which define these properties have been given Only a few of these systems have been proved to be complete The aim of this paper is to make a progress in the study of completeness for functional systems For this end, we use indexes as names for temporal flows and give new proofs of completeness Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works The only system considered which remains incomplete is the one which defines surjectivity, even if we consider a sequence of natural extensions of the previous one Copyright line will be provided by the publisher

Analyzing completeness of axiomatic functional systems for temporal × modal logics

We consider logics which define different properties of functions – such as injectivity, surjectivity, monotonicity, etc. – in the context of temporal×modal logic. In this type of logics, the possible worlds semantics is modified by considering each world as a temporal flow and using accessibility functions to represent the connection among them. This approach is adequate to model interactions between processes with clocks that can be either synchronized or not. We study the definability and give indexed axiomatic systems for these properties.

Functional systems in the context of temporal×modal logics with indexed flows

Combining modalities has proven to have interesting applications and many approaches that combine time with other types of modalities have been developed. One of these approaches uses accessibility functions between flows of time to study the basic properties of the functions, such as being total or partial, injective, surjective, etc. The completeness of certain systems expressing many of these properties, with the exception of surjectivity, has been proven. In this paper we propose a language with nominals to denote the initial and final sets of each function in a model in order to obtain a complete system for reasoning about surjective partial functions.

Completeness of a functional system for surjective functions

Two classical semantical approaches to studying logics which combine time and modality are the T /spl times/ W-frames and Kamp-frames (Thomason (1984)) In this paper we study a new kind of frame that extends the one introduced in Burrieza et al (2002) The motivation is twofold: theoretical, ie, representing properties of the basic theory of functions (definability); and practical, their use in computational applications (considering time-flows as memory of computers connected in a net, each computer with its own clock) Specifically, we present a temporal /spl times/ modal (labelled) logic, whose semantics are given by ind-functional frames in which accessibility functions are used in order to interconnect time-flows This way, we can: (i) specify to what time-flow we want to go; (ii) carry out different comparisons among worlds with different time measures; and (iii) define properties of certain kinds of functions (in particular, of total, injective, surjective, constant, increasing and decreasing functions), without the need to resort to second-order theories In addition, we define a minimal axiomatic system and give the completeness theorem (Henkin-style)

http://www.matap.uma.es/profesor/emilio/Time02.pdf

Indexed flows in temporal /spl times/ modal logic with functional semantics

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

E. Munoz

Author Tools

Chat about Author

Papers

Indexed flows in temporal /spl times/ modal logic with functional semantics