12 research outputs found
Extensions to the Estimation Calculus
Walther鈥檚 estimation calculus was designed to prove the termination of functional programs, and can also be used to solve the similar problem of proving the well-foundedness of induction rules. However, there are certain features of the goal formulae which are more common to the problem of induction rule well-foundedness than the problem of termination, and which the calculus cannot handle. We present a sound extension of the calculus that is capable of dealing with these features. The extension develops Walther鈥檚 concept of an argument bounded function in two ways: firstly, so that the function may be bounded below by its argument, and secondly, so that a bound may exist between two arguments of a predicate. Our calculus enables automatic proofs of the well-foundedness of a large class of induction rules not captured by the original calculus
Applications and extensions of context-sensitive rewriting
[EN] Context-sensitive rewriting is a restriction of term rewriting which is obtained by imposing replacement restrictions on the arguments of function symbols. It has proven useful to analyze computational properties of programs written in sophisticated rewriting-based programming languages such asCafeOBJ, Haskell, Maude, OBJ*, etc. Also, a number of extensions(e.g., to conditional rewritingor constrained equational systems) and generalizations(e.g., controlled rewritingor forbidden patterns) of context-sensitive rewriting have been proposed. In this paper, we provide an overview of these applications and related issues. (C) 2021 Elsevier Inc. All rights reserved.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Applications and extensions of context-sensitive rewriting. Journal of Logical and Algebraic Methods in Programming. 121:1-33. https://doi.org/10.1016/j.jlamp.2021.10068013312
ACUOS: A System for Order-Sorted Modular ACU Generalization
[ES] La generalizaci贸n, tambi茅n denominada anti-unificaci贸n, es la operaci贸n dual de la unificaci贸n. Dados dos t茅rminos t y t' , un generalizador es un t茅rmino t'' del cual t y t' son instancias de sustituci贸n. El concepto dual del unificador m谩s general (mgu) es el de generalizador menos general (lgg). En esta tesina extendemos el conocido algoritmo de generalizaci贸n sin tipos a, primero, una configuraci贸n order-sorted con sorts, subsorts y polimorfismo de subtipado; en segundo lugar, la extendemos para soportar generalizaci贸n m贸dulo teor铆as ecuacionales, donde los s铆mbolos de funci贸n pueden obedecer cualquier combinaci贸n de axiomas de asociatividad, conmutatividad e identidad (incluyendo el conjunto
vac铆o de dichos axiomas); y, en tercer lugar, a la combinaci贸n de ambos, que resulta en un algoritmo modular de generalizaci贸n order-sorted ecuacional. A diferencia de las configuraciones sin tipos, en nuestro marco te贸rico en general el lgg no es 煤nico, lo que se debe tanto al tipado como a los axiomas ecuacionales. En su lugar, existe un conjunto finito y m铆nimo de lggs, tales que cualquier otra generalizaci贸n tiene a alguno de ellos como instancia. Nuestros algoritmos de generalizaci贸n se expresan mediante reglas de inferencia para las cuales damos demostraciones de correcci贸n. Ello abre la puerta a nuevas aplicaciones en campos como la evaluaci贸n parcial, la s铆ntesis de programas, la
miner铆a de datos y la demostraci贸n de teoremas para sistemas de razonamiento ecuacional y lenguajes tipados basados en reglas tales como ASD+SDF, Elan, OBJ, CafeOBJ y Maude.
Esta tesis tambi茅n describe una herramienta para el c贸mputo automatizado de los generalizadores de un conjunto dado de estructuras en un lenguaje tipado m贸dulo un conjunto de axiomas dado. Al soportar la combinaci贸n modular de atributos ecuacionales de asociatividad, conmutatividad y existencia de elemento neutro (ACU) para s铆mbolos
de funci贸n arbitrarios, la generalizaci贸n ACU modular aporta suficiente poder expresivo a la
generalizaci贸n ordinaria para razonar sobre estructuras de datos tipadas tales como listas, conjuntos y multiconjuntos. La t茅cnica ha sido implementada con generalidad y eficiencia en el sistema ACUOS y puede ser f谩cilmente integrada con software de terceros.[EN] Generalization, also called anti-uni cation, is the dual of uni cation.
Given terms t and t
0
, a generalization is a term t
00
of which t and t
0
are
substitution instances. The dual of a most general uni er (mgu) is that
of least general generalization (lgg). In this thesis, we extend the known
untyped generalization algorithm to, rst, an order-sorted typed setting
with sorts, subsorts, and subtype polymorphism; second, we extend it to
work modulo equational theories, where function symbols can obey any
combination of associativity, commutativity, and identity axioms (includ-
ing the empty set of such axioms); and third, to the combination of both,
which results in a modular, order-sorted equational generalization algo-
rithm. Unlike the untyped case, there is in general no single lgg in our
framework, due to order-sortedness or to the equational axioms. Instead,
there is a nite, minimal set of lggs, so that any other generalization has
at least one of them as an instance. Our generalization algorithms are
expressed by means of inference systems for which we give proofs of cor-
rectness. This opens up new applications to partial evaluation, program
synthesis, data mining, and theorem proving for typed equational rea-
soning systems and typed rule-based languages such as ASF+SDF, Elan,
OBJ, Cafe-OBJ, and Maude.
This thesis also describes a tool for automatically computing the gen-
eralizers of a given set of structures in a typed language modulo a set
of axioms. By supporting the modular combination of associative, com-
mutative and unity (ACU) equational attributes for arbitrary function
symbols, modular ACU generalization adds enough expressive power to
ordinary generalization to reason about typed data structures such as
lists, sets and multisets. The ACU generalization technique has been
generally and e ciently implemented in the ACUOS system and can be
easily integrated with third-party software.Espert Real, J. (2012). ACUOS: A System for Order-Sorted Modular ACU Generalization. http://hdl.handle.net/10251/1921
Dynamic set reasoning: Specifying and optimizing monitor encodings
Specifying and monitoring temporal properties over sets on real-time embedded systems requires a logic that offers sufficient expressiveness and acceptable worst-case performance. If a system designer chooses to use a non-first-order logic, they sacrifice expressiveness; if they choose a first-order logic, they sacrifice performance. To mitigate this tradeoff, we present a first-order variant of Mission-time Linear Temporal Logic (MLTL) that can specify a wide range of behaviors and offers efficient monitoring of those behaviors. We also present a set of MLTL rewrite rules and use equality saturation to optimize MLTL monitor encodings automatically. After applying equality saturation to a set of human-authored MLTL formulas, our experimental evaluation found a ~35% average monitor size reduction
Foundations of Fuzzy Logic and Semantic Web Languages
This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic
Foundations of Fuzzy Logic and Semantic Web Languages
This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic