32,252 research outputs found
Semantic Criteria of Correct Formalization
This paper compares several models of formalization. It articulates criteria of correct formalization and identifies their problems. All of the discussed criteria are so called “semantic” criteria, which refer to the interpretation of logical formulas. However, as will be shown, different versions of an implicitly applied or explicitly stated criterion of correctness depend on different understandings of “interpretation” in this context
Constructing categories and setoids of setoids in type theory
In this paper we consider the problem of building rich categories of setoids,
in standard intensional Martin-L\"of type theory (MLTT), and in particular how
to handle the problem of equality on objects in this context. Any
(proof-irrelevant) family F of setoids over a setoid A gives rise to a category
C(A, F) of setoids with objects A. We may regard the family F as a setoid of
setoids, and a crucial issue in this article is to construct rich or large
enough such families. Depending on closure conditions of F, the category C(A,
F) has corresponding categorical constructions. We exemplify this with finite
limits. A very large family F may be obtained from Aczel's model construction
of CZF in type theory. It is proved that the category so obtained is isomorphic
to the internal category of sets in this model. Set theory can thus establish
(categorical) properties of C(A, F) which may be used in type theory. We also
show that Aczel's model construction may be extended to include the elements of
any setoid as atoms or urelements. As a byproduct we obtain a natural extension
of CZF, adding atoms. This extension, CZFU, is validated by the extended model.
The main theorems of the paper have been checked in the proof assistant Coq
which is based on MLTT. A possible application of this development is to
integrate set-theoretic and type-theoretic reasoning in proof assistants.Comment: 14 page
A Formal Approach based on Fuzzy Logic for the Specification of Component-Based Interactive Systems
Formal methods are widely recognized as a powerful engineering method for the
specification, simulation, development, and verification of distributed
interactive systems. However, most formal methods rely on a two-valued logic,
and are therefore limited to the axioms of that logic: a specification is valid
or invalid, component behavior is realizable or not, safety properties hold or
are violated, systems are available or unavailable. Especially when the problem
domain entails uncertainty, impreciseness, and vagueness, the appliance of such
methods becomes a challenging task. In order to overcome the limitations
resulting from the strict modus operandi of formal methods, the main objective
of this work is to relax the boolean notion of formal specifications by using
fuzzy logic. The present approach is based on Focus theory, a model-based and
strictly formal method for componentbased interactive systems. The contribution
of this work is twofold: i) we introduce a specification technique based on
fuzzy logic which can be used on top of Focus to develop formal specifications
in a qualitative fashion; ii) we partially extend Focus theory to a fuzzy one
which allows the specification of fuzzy components and fuzzy interactions.
While the former provides a methodology for approximating I/O behaviors under
imprecision, the latter enables to capture a more quantitative view of
specification properties such as realizability.Comment: In Proceedings FESCA 2015, arXiv:1503.0437
A Framework for Combining Defeasible Argumentation with Labeled Deduction
In the last years, there has been an increasing demand of a variety of
logical systems, prompted mostly by applications of logic in AI and other
related areas. Labeled Deductive Systems (LDS) were developed as a flexible
methodology to formalize such a kind of complex logical systems. Defeasible
argumentation has proven to be a successful approach to formalizing commonsense
reasoning, encompassing many other alternative formalisms for defeasible
reasoning. Argument-based frameworks share some common notions (such as the
concept of argument, defeater, etc.) along with a number of particular features
which make it difficult to compare them with each other from a logical
viewpoint. This paper introduces LDSar, a LDS for defeasible argumentation in
which many important issues concerning defeasible argumentation are captured
within a unified logical framework. We also discuss some logical properties and
extensions that emerge from the proposed framework.Comment: 15 pages, presented at CMSRA Workshop 2003. Buenos Aires, Argentin
Towards the Formal Reliability Analysis of Oil and Gas Pipelines
It is customary to assess the reliability of underground oil and gas
pipelines in the presence of excessive loading and corrosion effects to ensure
a leak-free transport of hazardous materials. The main idea behind this
reliability analysis is to model the given pipeline system as a Reliability
Block Diagram (RBD) of segments such that the reliability of an individual
pipeline segment can be represented by a random variable. Traditionally,
computer simulation is used to perform this reliability analysis but it
provides approximate results and requires an enormous amount of CPU time for
attaining reasonable estimates. Due to its approximate nature, simulation is
not very suitable for analyzing safety-critical systems like oil and gas
pipelines, where even minor analysis flaws may result in catastrophic
consequences. As an accurate alternative, we propose to use a
higher-order-logic theorem prover (HOL) for the reliability analysis of
pipelines. As a first step towards this idea, this paper provides a
higher-order-logic formalization of reliability and the series RBD using the
HOL theorem prover. For illustration, we present the formal analysis of a
simple pipeline that can be modeled as a series RBD of segments with
exponentially distributed failure times.Comment: 15 page
- …