The Experts below are selected from a list of 273 Experts worldwide ranked by ideXlab platform
Patricia Johann - One of the best experts on this subject based on the ideXlab platform.
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Combinatory Logic Approach to High Order E-Unification
2016Co-Authors: Patricia JohannAbstract:Le E be a first-order equational theory. A translation of typed higher-order E-unification problems into a typed Combinatory Logic framework is presented and justified. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modification of ordinary narrowing is shown to be a complete method for enumerating higher-order E-unifiers. In fact, we treat a more general problem, in which the types of terms contain type variables.
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A Combinator-based order-sorted higher-order unification algorithm
1999Co-Authors: Patricia JohannAbstract:This paper develops a sound and complete transformation-based algorithm forunification in an extensional order-sorted Combinatory Logic supporting constantoverloading and a higher-order sort concept. Appropriate notions of order-sortedweak equality and extensionality - reflecting order-sorted fij-equality in thecorresponding lambda calculus given by Johann and Kohlhase - are defined, andthe typed combinator-based higher-order unification techniques of Dougherty aremodified to accommodate unification with respect to the theory they generate. Thealgorithm presented here can thus be viewed as a Combinatory Logic counterpartto that of Johann and Kohlhase, as well as a refinement of that of Dougherty, andprovides evidence that Combinatory Logic is well-suited to serve as a framework forincorporating order-sorted higher-order reasoning into deduction systems aimingto capitalize on both the expressiveness of extensional higher-order Logic and theefficiency of order-sorted calculi.
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A Combinatory Logic approach to higher-order E-unification
Theoretical Computer Science, 1995Co-Authors: Daniel J. Dougherty, Patricia JohannAbstract:AbstractLet E be a first-order equational theory. A translation of higher-order E-unification problems into a Combinatory Logic framework is presented and justified. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modification of ordinary narrowing is shown to be a complete method for enumerating higher-order E-unifiers. In fact, we treat a more general problem, in which the types of terms contain type variables
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Normal Forms in Combinatory Logic
Notre Dame Journal of Formal Logic, 1994Co-Authors: Patricia JohannAbstract:Let R be a convergent term rewriting system, and let CR-equalityon (simply typed) Combinatory Logic terms be the equality induced by s?Requalityon terms of the (simply typed) lambda calculus under any of the standardtranslations between these two frameworks for higher-order reasoning. Wegeneralize the classical notion of strong reduction to a reduction relation whichgenerates CR-equality and whose irreducibles are exactly the translates of longsR-normal forms. The classical notion of strong normal form in CombinatoryLogic is also generalized, yielding yet another description of these translates.Their resulting tripartite characterization extends to the combined first-order algebraicand higher-order setting the classical Combinatory Logic descriptions ofthe translates of long s-normal forms in the lambda calculus. As a consequence,the translates of long sR-normal forms are easily seen to serve as canonicalrepresentatives for CR-equivalence classes of Combinatory Logic terms for nonempty,as well as for empty, R.
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a Combinatory Logic approach to higher order e unification extended abstract
Conference on Automated Deduction, 1992Co-Authors: Daniel J. Dougherty, Patricia JohannAbstract:Let E be a first-order equational theory. A translation of higher-order E-unification problems into a Combinatory Logic framework is presented and justified. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modification of ordinary narrowing is shown to be a complete method for enumerating higher-order E-unifiers. In fact, we treat a more general problem, in which the types of terms contain type variables.
Daniyar S Shamkanov - One of the best experts on this subject based on the ideXlab platform.
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strong normalization and confluence for reflexive Combinatory Logic
Workshop on Logic Language Information and Computation, 2011Co-Authors: Daniyar S ShamkanovAbstract:Reflexive Combinatory Logic RCL was introduced by S. Artemov as an extension of typed Combinatory Logic CL? capable to internalize its own derivations of typing judgments. It was designed as a basic theoretical prototype of functional programming languages extended by this kind of self-referential capacity. However, its operational aspects remained to be clarified. We study reductions for reflexive Combinatory Logic and prove strong normalization and confluence properties.
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WoLLIC - Strong normalization and confluence for reflexive Combinatory Logic
Logic Language Information and Computation, 2011Co-Authors: Daniyar S ShamkanovAbstract:Reflexive Combinatory Logic RCL was introduced by S. Artemov as an extension of typed Combinatory Logic CL? capable to internalize its own derivations of typing judgments. It was designed as a basic theoretical prototype of functional programming languages extended by this kind of self-referential capacity. However, its operational aspects remained to be clarified. We study reductions for reflexive Combinatory Logic and prove strong normalization and confluence properties.
Jakob Rehof - One of the best experts on this subject based on the ideXlab platform.
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automatic composition of rough solution possibilities in the target planning of factory planning projects by means of Combinatory Logic
Leveraging Applications of Formal Methods, 2018Co-Authors: Jan Winkels, Jakob Rehof, Tristan Schäfer, Julian Graefenstein, David Scholz, Michael HenkeAbstract:Increasing competition, stronger customer focus, shorter product lifecycles and accelerated technoLogical developments imply that companies are faced with the challenge of adapting their own production to the circumstances at ever shorter intervals. The factory planning project is becoming increasingly complex, but there is less and less time available for adaptation. Particularly in the initial planning phase, targets are defined without reliable planning information for the further course, which have far-reaching consequences for the outcome of a successful planning. This paper shows a possibility to generate meaningful solution alternatives at an early stage of the target planning in order to enable an efficient planning process in terms of time and costs. With the help of a constraint-based variant compilation on the basis of previously defined target and frame parameters as well as existing information on the current factory system, various possible solution variants for target planning are to be created. A specific use case scenario was used to develop and test the presented methodology. By comparing combinations of the most diverse possible solutions, the use of a Combinatory Logic approach enables the first rough and plausible solution variants to be generated automatically, on the basis of which the detailed planning process for achieving the determined solution variant can be created. This way, planning bottlenecks due to the wrong choice of variants as well as large time expenditure for the creation of solution variants can be avoided.
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ISoLA (4) - Automatic Composition of Rough Solution Possibilities in the Target Planning of Factory Planning Projects by Means of Combinatory Logic
Lecture Notes in Computer Science, 2018Co-Authors: Jan Winkels, Jakob Rehof, Tristan Schäfer, Julian Graefenstein, David Scholz, Michael HenkeAbstract:Increasing competition, stronger customer focus, shorter product lifecycles and accelerated technoLogical developments imply that companies are faced with the challenge of adapting their own production to the circumstances at ever shorter intervals. The factory planning project is becoming increasingly complex, but there is less and less time available for adaptation. Particularly in the initial planning phase, targets are defined without reliable planning information for the further course, which have far-reaching consequences for the outcome of a successful planning. This paper shows a possibility to generate meaningful solution alternatives at an early stage of the target planning in order to enable an efficient planning process in terms of time and costs. With the help of a constraint-based variant compilation on the basis of previously defined target and frame parameters as well as existing information on the current factory system, various possible solution variants for target planning are to be created. A specific use case scenario was used to develop and test the presented methodology. By comparing combinations of the most diverse possible solutions, the use of a Combinatory Logic approach enables the first rough and plausible solution variants to be generated automatically, on the basis of which the detailed planning process for achieving the determined solution variant can be created. This way, planning bottlenecks due to the wrong choice of variants as well as large time expenditure for the creation of solution variants can be avoided.
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Combinatory Logic synthesizer
Leveraging Applications of Formal Methods, 2014Co-Authors: Jan Bessai, Boris Dudder, Moritz Martens, Andrej Dudenhefner, Jakob RehofAbstract:We present Combinatory Logic Synthesizer CLS, a type-based tool to automatically compose larger systems from repositories of components. We overview its underlying theory, Combinatory Logic with intersection types, and exemplify its application to synthesis. We describe features and architecture of the tool and our plans for its ongoing and future development. Finally, we present some use cases in ongoing work, especially in the context of synthesis for Object Oriented Software.
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ISoLA (1) - Combinatory Logic Synthesizer
Leveraging Applications of Formal Methods Verification and Validation. Technologies for Mastering Change, 2014Co-Authors: Jan Bessai, Boris Dudder, Moritz Martens, Andrej Dudenhefner, Jakob RehofAbstract:We present Combinatory Logic Synthesizer CLS, a type-based tool to automatically compose larger systems from repositories of components. We overview its underlying theory, Combinatory Logic with intersection types, and exemplify its application to synthesis. We describe features and architecture of the tool and our plans for its ongoing and future development. Finally, we present some use cases in ongoing work, especially in the context of synthesis for Object Oriented Software.
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Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis
Electronic Proceedings in Theoretical Computer Science, 2013Co-Authors: Boris Dudder, Moritz Martens, Jakob Rehof, Oliver Garbe, Pawel UrzyczynAbstract:We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on Combinatory Logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation {\textemdash} is there a Combinatory term e with type tau relative to an environment Gamma? {\textemdash} can be used to synthesize compositions. Here, Gamma represents the repository in the form of typed combinators, tau specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.
Jean-pierre Desclés - One of the best experts on this subject based on the ideXlab platform.
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Aspecto-Temporal Meanings Analysed by Combinatory Logic
Journal of Logic Language and Information, 2014Co-Authors: Jean-pierre Desclés, Anca Christine PascuAbstract:What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations (GRACE) (Desclés and Ro in Math Sci Hum 194:39–70, 2011 ), using the applicative formalism, functional types of categorial grammars and Combinatory Logic (CL) (Curry and Feys in Combinatory Logic. North-Holland Publishing, Amsterdam, 1958 ). In the enunciative theory (Benveniste in Problèmes de linguistique générale, 1, 2. Gallimard, Paris, 1974 ; Culioli in Formalisation et opérations de repérage, tome 2. Ophrys, Paris, 1999 ; Desclés in Une articulation entre syntaxe et sémantique cognitive: la grammaire applicative et cognitive, mémoires de la société de linguistique de Paris, nouvelle série, tome XX, l’architecture des théories, les modules et leurs interfaces. Peeters, Louvain, 2011 ) and following (Bally in Linguistique générale et linguistique française. Berne, Franke, 1965 ), an utterance can be decomposed into two components: a modus and a dictum (or a proposition). In GRACE, the modus is a complex operator applied to a proposition (a dictum ) and is generated from more elementary operators of the categories of tense, aspect, and modality. The dictum is a proposition generated by a predicative relation. In this way, we can attribute a semantic meaning to different grammatical aspecto-temporal operators. The applicative expressions of CL can be easily translated into a functional programming language such as HASKELL or CAML (Ro in Les référentiels et opérateurs aspecto-temporels: définitions, formalisation logique et informatique. PhD thesis, Université de Paris-Sorbonne, Paris, 2012 ).
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Aspecto-Temporal Meanings Analysed by Combinatory Logic
Journal of Logic Language and Information, 2014Co-Authors: Jean-pierre Desclés, Anca PascuAbstract:What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations (GRACE) (Descles and Ro in Math Sci Hum 194:39---70, 2011), using the applicative formalism, functional types of categorial grammars and Combinatory Logic (CL) (Curry and Feys in Combinatory Logic. North-Holland Publishing, Amsterdam, 1958). In the enunciative theory (Benveniste in Problemes de linguistique generale, 1, 2. Gallimard, Paris, 1974; Culioli in Formalisation et operations de reperage, tome 2. Ophrys, Paris, 1999; Descles in Une articulation entre syntaxe et semantique cognitive: la grammaire applicative et cognitive, memoires de la societe de linguistique de Paris, nouvelle serie, tome XX, l'architecture des theories, les modules et leurs interfaces. Peeters, Louvain, 2011) and following (Bally in Linguistique generale et linguistique francaise. Berne, Franke, 1965), an utterance can be decomposed into two components: a modus and a dictum (or a proposition). In GRACE, the modus is a complex operator applied to a proposition (a dictum) and is generated from more elementary operators of the categories of tense, aspect, and modality. The dictum is a proposition generated by a predicative relation. In this way, we can attribute a semantic meaning to different grammatical aspecto-temporal operators. The applicative expressions of CL can be easily translated into a functional programming language such as HASKELL or CAML (Ro in Les referentiels et operateurs aspecto-temporels: definitions, formalisation logique et informatique. PhD thesis, Universite de Paris-Sorbonne, Paris, 2012).
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FLAIRS Conference - Reasoning in Natural Language in using Combinatory Logic and Topology An example with aspect and temporal relations
2010Co-Authors: Jean-pierre DesclésAbstract:We are studying how Curry’s Combinatory Logic can be used for giving an adequate analysis of different gram matical problems such as diatheses, tenses and aspects, and lexical analyses by formal representations of meanings of verbal predicates and prepositions. The paper intends to show how Combinatory Logic can solve on the one hand, the formal representations of tenses and aspects in natural languages with the help of the topology of intervals and, on the other hand, the problem of the synthesis of a lexical predicate from a formal description of its meaning by means of a semantic cognitive scheme (SCS). We want to explain, in following an example, how can be explained the “natural” inference between two utterances like John took the Mary’s pen. > Now, John has got the pen.
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reasoning in natural language in using Combinatory Logic and topology an example with aspect and temporal relations
The Florida AI Research Society, 2010Co-Authors: Jean-pierre DesclésAbstract:We are studying how Curry’s Combinatory Logic can be used for giving an adequate analysis of different gram matical problems such as diatheses, tenses and aspects, and lexical analyses by formal representations of meanings of verbal predicates and prepositions. The paper intends to show how Combinatory Logic can solve on the one hand, the formal representations of tenses and aspects in natural languages with the help of the topology of intervals and, on the other hand, the problem of the synthesis of a lexical predicate from a formal description of its meaning by means of a semantic cognitive scheme (SCS). We want to explain, in following an example, how can be explained the “natural” inference between two utterances like John took the Mary’s pen. > Now, John has got the pen.
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FLAIRS Conference - Categorial Grammars, Combinatory Logic and the Korean Language Processing
2008Co-Authors: Juyeon Kang, Jean-pierre DesclésAbstract:In this paper we propose a new approach to Categorial Grammars based on Combinatory Logic to solve some syntactic and semantic problems in the Korean language processing. We handle particularly the problems of cases, free word order structure and coordination by developing a formalism of the extended Categorial Grammar that was originally introduced by J.-P. Descles, and I. Biskri. We call this extended Categorial Grammar “Applicative and Combinatory Categorial Grammar (ACCG)” . T he ACCG formalism allows us to analyze syntactically and semantically the cases in Korean, in particular the linguistic phenomenon of double cases. In spite of the importance of the cases in the processing of the Korean language, this topic has not been well studied in view to its automatic processing and there are still many difficulties in parsing Korean texts. This article shows some robust solutions for the analysis of the free word order structure and of the coordination by introducing combinators, such as B, C*, Φ, of Combinatory Logic developed by H.-B. Curry and R. Feys.
Pawel Urzyczyn - One of the best experts on this subject based on the ideXlab platform.
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Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis
Electronic Proceedings in Theoretical Computer Science, 2013Co-Authors: Boris Dudder, Moritz Martens, Jakob Rehof, Oliver Garbe, Pawel UrzyczynAbstract:We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on Combinatory Logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation {\textemdash} is there a Combinatory term e with type tau relative to an environment Gamma? {\textemdash} can be used to synthesize compositions. Here, Gamma represents the repository in the form of typed combinators, tau specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.
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using inhabitation in bounded Combinatory Logic with intersection types for composition synthesis
Electronic Proceedings in Theoretical Computer Science, 2013Co-Authors: Boris Dudder, Moritz Martens, Jakob Rehof, Oliver Garbe, Pawel UrzyczynAbstract:We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on Combinatory Logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation — is there a Combinatory term e with type t relative to an environment G? — can be used to synthesize compositions. Here, G represents the repository in the form of typed combinators, t specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.
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bounded Combinatory Logic
Computer Science Logic, 2012Co-Authors: Boris Dudder, Moritz Martens, Jakob Rehof, Pawel UrzyczynAbstract:In Combinatory Logic one usually assumes a fixed set of basic combinators (axiom schemes), usually K and S. In this setting the set of provable formulas (inhabited types) is PSPACE-complete in simple types and undecidable in intersection types. When arbitrary sets of axiom schemes are considered, the inhabitation problem is undecidable even in simple types (this is known as Linial-Post theorem). k-bounded Combinatory Logic with intersection types arises from Combinatory Logic by imposing the bound k on the depth of types (formulae) which may be substituted for type variables in axiom schemes. We consider the inhabitation (provability) problem for k-bounded Combinatory Logic: Given an arbitrary set of typed combinators and a type tau, is there a Combinatory term of type tau in k-bounded Combinatory Logic? Our main result is that the problem is (k+2)-EXPTIME complete for k-bounded Combinatory Logic with intersection types, for every fixed k (and hence non-elementary when k is a parameter). We also show that the problem is EXPTIME-complete for simple types, for all k. Theoretically, our results give new insight into the expressive power of intersection types. From an application perspective, our results are useful as a foundation for composition synthesis based on Combinatory Logic.
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CSL - Bounded Combinatory Logic
2012Co-Authors: Boris Dudder, Moritz Martens, Jakob Rehof, Pawel UrzyczynAbstract:In Combinatory Logic one usually assumes a fixed set of basic combinators (axiom schemes), usually K and S. In this setting the set of provable formulas (inhabited types) is PSPACE-complete in simple types and undecidable in intersection types. When arbitrary sets of axiom schemes are considered, the inhabitation problem is undecidable even in simple types (this is known as Linial-Post theorem). k-bounded Combinatory Logic with intersection types arises from Combinatory Logic by imposing the bound k on the depth of types (formulae) which may be substituted for type variables in axiom schemes. We consider the inhabitation (provability) problem for k-bounded Combinatory Logic: Given an arbitrary set of typed combinators and a type tau, is there a Combinatory term of type tau in k-bounded Combinatory Logic? Our main result is that the problem is (k+2)-EXPTIME complete for k-bounded Combinatory Logic with intersection types, for every fixed k (and hence non-elementary when k is a parameter). We also show that the problem is EXPTIME-complete for simple types, for all k. Theoretically, our results give new insight into the expressive power of intersection types. From an application perspective, our results are useful as a foundation for composition synthesis based on Combinatory Logic.
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finite Combinatory Logic with intersection types
International Conference on Typed Lambda Calculi and Applications, 2011Co-Authors: Jakob Rehof, Pawel UrzyczynAbstract:Combinatory Logic is based on modus ponens and a schematic (polymorphic) interpretation of axioms. In this paper we propose to consider expressive Combinatory Logics under the restriction that axioms are not interpreted schematically but "literally", corresponding to a monomorphic interpretation of types. We thereby arrive at finite Combinatory Logic, which is strictly finitely axiomatisable and based solely on modus ponens. We show that the provability (inhabitation) problem for finite Combinatory Logic with intersection types is Exptime-complete with or without subtyping. This result contrasts with the general case, where inhabitation is known to be Expspace-complete in rank 2 and undecidable for rank 3 and up. As a by-product of the considerations in the presence of subtyping, we show that standard intersection type subtyping is in Ptime. From an application standpoint, we can consider intersection types as an expressive specification formalism for which our results show that functional composition synthesis can be automated.