Automated Reasoning in Some Local Extensions of Ordered Structures

Sofronie-Stokkermans, Viorica; Ihlemann, Carsten

doi:10.1109/ismvl.2007.10

Cited by 24 publications

(27 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following theorem extends known results on local extensions with monotone functions [7,16] to the case of preorders and bounded (semi-)prelattices:…”

Section: Complete Reasoning About Many-invocation Axiomssupporting

confidence: 68%

“…They have proved useful in the verification of parametrized systems [9] and properties of data structures [5,15], and in reasoning about certain properties of numerical functions [14] and functions in ordered domains [16]. Algebraic data types with size functions are shown to be decidable in [19].…”

Section: Related Workmentioning

confidence: 99%

“…We thank Viorica Sofronie-Stokkermans for detailed comments on drafts of this paper, as well as the original suggestion to generalize the monotonicity axiom from [16] to the version in [7]. We thank Philippe Suter for discussions related to Section 4.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Towards Complete Reasoning about Axiomatic Specifications

Jacobs

Kunčak

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. To support verification of expressive properties of functional programs, we consider algebraic style specifications that may relate multiple user-defined functions, and compare multiple invocations of a function for different arguments. We present decision procedures for reasoning about such universally quantified properties of functional programs, using local theory extension methodology. We establish new classes of universally quantified formulas whose satisfiability can be checked in a complete way by finite quantifier instantiation. These classes include single-invocation axioms that generalize standard function contracts, but also certain many-invocation axioms, specifying that functions satisfy congruence, injectivity, or monotonicity with respect to abstraction functions, as well as conjunctions of some of these properties. These manyinvocation axioms can specify correctness of abstract data type implementations as well as certain information-flow properties. We also present a decidability-preserving construction that enables the same function to be specified using different classes of decidable specifications on different partitions of its domain.

show abstract

“…The following theorem extends known results on local extensions with monotone functions [7,16] to the case of preorders and bounded (semi-)prelattices:…”

Section: Complete Reasoning About Many-invocation Axiomssupporting

confidence: 68%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Towards Complete Reasoning about Axiomatic Specifications

Jacobs

Kunčak

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…By the results in [34] such extensions are also local. In fact, both extensions satisfy condition Comp f .…”

Section: 7mentioning

confidence: 80%

“…(5) Generalized monotonicity conditions -combinations of monotonicity in some arguments and antitonicity in other arguments -as well as extensions with functions defined by case distinction (over a disjoint set of conditions) were studied in [34]. We now present some more examples which were studied in [30].…”

Section: Examples Of Local Theory Extensionsmentioning

confidence: 99%

On Interpolation and Symbol Elimination in Theory Extensions

Sofronie-Stokkermans

2016

Automated Reasoning

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory T0 with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which we can perform such tasks in a hierarchical way, relying on existing mechanisms for symbol elimination in T0. This is for instance possible if the base theory allows quantifier elimination. We analyze possibilities of extending such methods to situations in which the base theory does not allow quantifier elimination but has a model completion which does. We illustrate the method on various examples.

show abstract

On P-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics $$\mathcal{E}\mathcal{L}, \mathcal{E}\mathcal{L}^+$$

Peuter,

Sofronie-Stokkermans,

Thunert

2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We study the P-interpolation property for certain local theory extensions, and use these results for proving $$\le $$ ≤ -interpolation in classes of semilattices with monotone operators. For computing the $$\le $$ ≤ -interpolating terms, we use a hierarchic approach. We use these results for the study of $$\sqsubseteq $$ ⊑ -interpolation in the description logics $$\mathcal{E}\mathcal{L}$$ E L and $$\mathcal{E}\mathcal{L}^+$$ E L + .

show abstract

Automated Reasoning in Some Local Extensions of Ordered Structures

Cited by 24 publications

References 28 publications

Towards Complete Reasoning about Axiomatic Specifications

Towards Complete Reasoning about Axiomatic Specifications

On Interpolation and Symbol Elimination in Theory Extensions

On P-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics $$\mathcal{E}\mathcal{L}, \mathcal{E}\mathcal{L}^+$$

Contact Info

Product

Resources

About