Synthesis of models for order-sorted first-order theories using linear algebra and constraint solving

Lucas, Salvador

doi:10.4204/eptcs.200.3

Cited by 3 publications

(13 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [10] we have shown that convex domains [12] provide an appropriate basis to the automatic definition of algebras and structures that can be used in program analysis with order-sorted first-order specifications. In the following definition, vectors x, y ∈ R n are compared using the coordinate-wise extension of the ordering ≥ among numbers which, by abuse, we denote using ≥ as well:…”

Section: Interpreting Predicates Using Convex Domainsmentioning

confidence: 99%

“…In [10] no procedure for the automatic generation of predicate interpretations was given. We solve this problem by providing (parametric) interpretations for predicate symbols P of any rank w ∈ S + .…”

Section: Interpreting Predicates Using Convex Domainsmentioning

confidence: 99%

“…In [6] Order-Sorted First-Order Logic (OS-FOL) is proposed as a sufficiently general and expressive framework to represent declarative programs, semantics of programming languages, and program properties (see Section 3). In [10] we show how to systematically generate models for OS-FOL theories by using the convex polytopic domains introduced in [12]. In Section 4 we extend the work in [10] to generate appropriate interpretations of predicate symbols that can be then used to synthesize a model for a given OS-FOL theory S.…”

Section: Introductionmentioning

confidence: 99%

“…In [10] we show how to systematically generate models for OS-FOL theories by using the convex polytopic domains introduced in [12]. In Section 4 we extend the work in [10] to generate appropriate interpretations of predicate symbols that can be then used to synthesize a model for a given OS-FOL theory S.…”

Section: Introductionmentioning

confidence: 99%

“…Section 6 illustrates the use of the new developments to prove operational termination of PATH in the OT Framework. Automation of the analysis is achieved by using AGES [8], a web-based tool that implements the techniques in [10] and also in this paper. Section 7 concludes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Use of Logical Models for Proving Operational Termination in General Logics

Lucas

2016

Rewriting Logic and Its Applications

Self Cite

View full text Add to dashboard Cite

Abstract. A declarative programming language is based on some logic L and its operational semantics is given by a proof calculus which is often presented in a natural deduction style by means of inference rules. Declarative programs are theories S of L and executing a program is proving goals ϕ in the inference system I(S) associated to S as a particularization of the inference system of the logic. The usual soundness assumption for L implies that every model A of S also satisfies ϕ. In this setting, the operational termination of a declarative program is quite naturally defined as the absence of infinite proof trees in the inference system I(S). Proving operational termination of declarative programs often involves two main ingredients: (i) the generation of logical models A to abstract the program execution (i.e., the provability of specific goals in I(S)), and (ii) the use of well-founded relations to guarantee the absence of infinite branches in proof trees and hence of infinite proof trees, possibly taking into account the information about provability encoded by A. In this paper we show how to deal with (i) and (ii) in a uniform way. The main point is the synthesis of logical models where well-foundedness is a side requirement for some specific predicate symbols.

show abstract

Section: Interpreting Predicates Using Convex Domainsmentioning

confidence: 99%

Section: Interpreting Predicates Using Convex Domainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Use of Logical Models for Proving Operational Termination in General Logics

Lucas

2016

Rewriting Logic and Its Applications

Self Cite

View full text Add to dashboard Cite

show abstract

Rewriting Logic and Its Applications

Lucanu¹

2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A declarative programming language is based on some logic L and its operational semantics is given by a proof calculus which is often presented in a natural deduction style by means of inference rules. Declarative programs are theories S of L and executing a program is proving goals ϕ in the inference system I(S) associated to S as a particularization of the inference system of the logic. The usual soundness assumption for L implies that every model A of S also satisfies ϕ. In this setting, the operational termination of a declarative program is quite naturally defined as the absence of infinite proof trees in the inference system I(S). Proving operational termination of declarative programs often involves two main ingredients: (i) the generation of logical models A to abstract the program execution (i.e., the provability of specific goals in I(S)), and (ii) the use of well-founded relations to guarantee the absence of infinite branches in proof trees and hence of infinite proof trees, possibly taking into account the information about provability encoded by A. In this paper we show how to deal with (i) and (ii) in a uniform way. The main point is the synthesis of logical models where well-foundedness is a side requirement for some specific predicate symbols.

show abstract

Automatic Synthesis of Logical Models for Order-Sorted First-Order Theories

Lucas

Gutiérrez

2017

J Autom Reasoning

Self Cite

View full text Add to dashboard Cite

In program analysis, the synthesis of models of logical theories representing the program semantics is often useful to prove program properties. We use Order-Sorted First-Order Logic as an appropriate framework to describe the semantics and properties of programs as given theories. Then we investigate the automatic synthesis of models for such theories. We use convex polytopic domains as a flexible approach to associate different domains to different sorts. We introduce a framework for the piecewise definition of functions and predicates. We develop its use with linear expressions (in a wide sense, including linear transformations represented as matrices) and inequalities to specify functions and predicates. In this way, algorithms and tools from linear algebra and arithmetic constraint solving (e.g., SMT) can be used as a backend for an efficient implementation.

show abstract

Synthesis of models for order-sorted first-order theories using linear algebra and constraint solving

Cited by 3 publications

References 14 publications

Use of Logical Models for Proving Operational Termination in General Logics

Use of Logical Models for Proving Operational Termination in General Logics

Rewriting Logic and Its Applications

Automatic Synthesis of Logical Models for Order-Sorted First-Order Theories

Contact Info

Product

Resources

About