Abstract. In this paper we will discuss two different translations between RDF (Resource Descript... more Abstract. In this paper we will discuss two different translations between RDF (Resource Description Format) and Conceptual Graphs (CGs). These translations will allow tools like Cogui and Cogitant to be able to import and export RDF(S) documents. The first translation is sound and complete from a reasoning view point but is not visual nor a representation in the spirit of Conceptual Graphs (CGs). The second translation has the advantage of being natural and fully ex-ploiting the CG features, but, on the other hand it does not apply to the whole RDF(S). We aim this paper as a preliminary report of ongoing work looking in detail at different pro and the cons of each approach. 1 Introduction and motivation
We consider positive rules in which the conclusion may contain existentially quantified variables... more We consider positive rules in which the conclusion may contain existentially quantified variables, which makes reasoning tasks (such as conjunctive query answering or entailment) undecidable. These rules, called 89-rules, have the same logical form as tuple-generating dependencies in databases and as conceptual graph rules. The aim of this paper is to provide a clearer picture of the frontier between decidability and non-decidability of reasoning with these rules. Previous known decidable classes were based on forward chaining. On the one hand we extend these classes, on the other hand we introduce decidable classes based on backward chaining. A side result is the definition of a backward mechanism that takes the complex structure of 89-rule conclusions into account. We classify all known decidable classes by inclusion. Then, we study the question of whether the union of two decidable classes remains decidable and show that the answer is negative, except for one class and a still op...
This paper reports a collective reflection led in our team about conceptual graph benchmarks. We ... more This paper reports a collective reflection led in our team about conceptual graph benchmarks. We tackle four issues for which agreement should be obtained before benchmarks can be built: what are the fragments of CGs considered? How is information exchanged? What are the problems to be solved? What kinds of tool properties are eval- uated by the benchmarks? We define a basic building block built upon simple conceptual graphs. Finally we propose to provide a first bench- mark adapted from an industrial case study. This benchmark is composed on very simple structures and should allow to focus on interoperability issues.
The research works on knowledge validation aim at enhancing the quality of knowledge bases. The c... more The research works on knowledge validation aim at enhancing the quality of knowledge bases. The conceptual graph model is a knowledge representation model which belongs to the family of the semantic networks. We give a solution to validate semantically a knowledge base expressed in terms of conceptual graphs. The semantic validation of a knowledge base consists in checking that the
This paper reports a collective reflection led in our team about conceptual graph benchmarks. We ... more This paper reports a collective reflection led in our team about conceptual graph benchmarks. We tackle four issues for which agreement should be obtained before benchmarks can be built: what are the fragments of CGs considered? How is information exchanged? What are the problems to be solved? What kinds of tool properties are evaluated by the benchmarks? We define a basic building block built upon simple conceptual graphs. Finally we propose to provide a first benchmark adapted from an industrial case study. This benchmark is composed on very simple structures and should allow to focus on interoperability issues.
Abstract. In this paper we will discuss two different translations between RDF (Resource Descript... more Abstract. In this paper we will discuss two different translations between RDF (Resource Description Format) and Conceptual Graphs (CGs). These translations will allow tools like Cogui and Cogitant to be able to import and export RDF(S) documents. The first translation is sound and ...
Conceptual Graphs offer an attractive and intuitive formalism for knowledge representation in Art... more Conceptual Graphs offer an attractive and intuitive formalism for knowledge representation in Artificial Intelligence. The formalism calls for efficient systems of reasoning. Projection is one such tool for a language limited to conjunction and existential quantification (Simple Conceptual Graphs). Projection is very efficient for certain classes of Conceptual Graphs and offers an original approach to deduction: the perspective of graph matching. The aim of this paper is twofold: Propose an efficient analytic deduction system that combines analytic tableaux with projection for a language of Conceptual Graphs extended to all non functional First-Order Logic formulae and compare this method with the one introduced in [1] for Simple Conceptual Graph rules.
Simple conceptual graphs can be seen as a very basic description logic, allowing however for answ... more Simple conceptual graphs can be seen as a very basic description logic, allowing however for answering conjunctive queries. In the first part of this paper, we translate some results obtained for conceptual graph rules of form "if A then B" into an equivalent DL-based formalism. Then we show that, our algorithms can automatically decide in some cases whether a given DL has the FOL-reducibility property, provided that the semantics of its constructors can be expressed by rules. 2 DL-SG: conjunctive queries, but lite TBox ... 2.1 DL-SG syntax and semantics A vocabulary V is the union of pairwise disjoint sets N , R 1 ,. .. , R k where N contains individual names and R i contains role names of arity i. Role names of arity 1 are called concept names (C = R 1). The set of concept names contains a distinguished element, ⊥ (the absurd concept name). We also consider a set X of variables, disjoint from names of V. The set T = N ∪ X is the set of terms. Definition 1 (Primitive TBox). A primitive TBox is a set of inclusion assertions of form R R where R and R = ⊥ are role names with the same arity. Definition 2 (Unrestricted ABox). An unrestricted ABox is a set of membership assertions of form r(t 1 ,. .. , t p) where r is a role name of arity p (i.e. a concept name if p = 1) and the t i are terms. Definition 3 (DL-SG knowledge bases and queries). A DL-SG knowledge base is an ordered pair K = (T, A) where T is a primitive TBox and A is an unrestricted ABox. A query is an unrestricted ABox. We note V(K), N (K), R i (K), X (K), T (K) the sets of names, individual names, role names, variables and terms contained in a KB K. An interpretation is an ordered pair I = (∆ I ,. I) where ∆ I is a non-empty set called the interpretation domain, and the interpretation function. I maps each individual name n ∈ N to an element n I of ∆ I , and each role name r of arity k of R k to a subset r I of (∆ I) k (a concept name is mapped to a subset of ∆ I , and ⊥ I = ∅). Definition 4 (Model of a primitive TBox). Let T be a primitive TBox. An interpretation I is a model of T iff for every R R of T , R I ⊆ R I. Definition 5 (Model of an unrestricted ABox). Let A be an unrestricted ABox. An interpretation I is a model of A iff there is a mapping µ : T (A) → ∆ I (called a proof of A in I) such that (i) ∀n ∈ N (A), µ(n) = n I ; and (ii) ∀r(t 1 ,. .. , t k) ∈ A, (µ(t 1),. .. , µ(t k)) ∈ r I. An unrestricted ABox is indeed the linear encoding, with the same semantics, of a positive, conjunctive, existential FOL formula without function symbols, while the TBox encodes implications of form ∀x 1. .. ∀x k (r(x 1 ,. .. , x k) → r (x 1 ,. .. , x k)). A primitive TBox has the same semantics as a CG support, while an unrestricted ABox has the same semantics as a simple CG. This is why the soundness and completeness results presented in this paper can be stated as a direct translation of the CG versions in which they have been proven. Note that (T, A) can also be seen as a relational database by freezing its variables. An interpretation is a model of a KB (T, A) iff it is a model of T and A.
Proceedings of the 6th International Conference on Conceptual Structures Theory Tools and Applications, 1998
... Our research group considers the CG model [16] as a declarative model where knowledge is sole... more ... Our research group considers the CG model [16] as a declarative model where knowledge is solely represented by labeled graphs and reasoning is can be done by labeled graphs operations [3]. In a first stage, such a model, the "simple conceptual graph" (SCG) model has ...
ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des base... more ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des bases de connaissances. Le modèle des graphes conceptuels est un modèle de représentation des connaissances de la famille des réseaux sémantiques, fondé sur la théorie des graphes et sur la logique du premier ordre. Nous proposons une solution pour valider sémantiquement une base de connaissances composée de graphes conceptuels. La validation sémantique d'une base de connaissance consiste à confronter ses connaissances à des contraintes certifiées fiables. Nous proposons d'utiliser des contraintes descriptives, exprimées sous forme de graphes conceptuels, qui permettent de poser des conditions sur la représentation de certaines connaissance dans la base. Ces contraintes introduisent une notion de cardinalités, et sont soit minimales, soit maximales. Elles permettent respectivement d'exprimer "si A, alors au moins ou au plus n fois B". La satisfaction de ces contraintes par une base de connaissances repose sur l'utilisation de l'opération de base du modèle des graphes conceptuels : la projection.
In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason-... more In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason- ing tasks (as deduction) non-decidable. These rules have the same logical form as TGD (tuple- generating dependencies) in databases and as con- ceptual graph rules. We extend known decidable cases by combining backward and forward chain- ing schemes, in association with a graph that cap- tures exactly the notion of dependency between rules. Finally, we draw a map of known decidable cases, including an extension obtained by combin- ing our approach with very recent results on TGD.
We study the properties of semantic consequence in a particular subset of first-order logic with ... more We study the properties of semantic consequence in a particular subset of first-order logic with equality and no function symbols, under the unique name assumption. Formulas in this subset of logic are rules of form $\forall \vec x (H \rightarrow \exists \vec y C) where the hypothesis $H$ and the conclusion $C$ are conjunctions of atoms (possibly with equality), $\vec x$ contains the variables in $H$ and $\vec y$ the variables in $C$ that are not in $H$. This subset is particularly expressive since it can encode a universal Turing machine, at the cost of decidability of reasoning. We propose new decidable subclasses of this problem, by combining restrictions on both the structure of the rules themselves and the structure of the interactions between rules, encoded in the graph of rule dependencies. The most general decidable subclass presented here is based on a mixed forward/backward chaining algorithm. Finally, we relate our rules to other notions (tuple-generating dependencies in ...
Simple conceptual graphs can be seen as a very basic de- scription logic, allowing however for an... more Simple conceptual graphs can be seen as a very basic de- scription logic, allowing however for answering conjunctive queries. In the rst part of this paper, we translate some results obtained for con- ceptual graph rules of form \if A then B" into an equivalent DL-based formalism. Then we show that, our algorithms can automatically decide in some cases whether
Simple conceptual graphs can be seen as a very basic description logic, allowing however for answ... more Simple conceptual graphs can be seen as a very basic description logic, allowing however for answering conjunctive queries. In the first part of this paper, we translate some results obtained for conceptual graph rules of form "if A then B" into an equivalent DL-based formalism. Then we show that, our algorithms can automatically decide in some cases whether a given DL has the FOL-reducibility property, provided that the semantics of its constructors can be expressed by rules. 2 DL-SG: conjunctive queries, but lite TBox ... 2.1 DL-SG syntax and semantics A vocabulary V is the union of pairwise disjoint sets N , R 1 ,. .. , R k where N contains individual names and R i contains role names of arity i. Role names of arity 1 are called concept names (C = R 1). The set of concept names contains a distinguished element, ⊥ (the absurd concept name). We also consider a set X of variables, disjoint from names of V. The set T = N ∪ X is the set of terms. Definition 1 (Primitive TBox). A primitive TBox is a set of inclusion assertions of form R R where R and R = ⊥ are role names with the same arity. Definition 2 (Unrestricted ABox). An unrestricted ABox is a set of membership assertions of form r(t 1 ,. .. , t p) where r is a role name of arity p (i.e. a concept name if p = 1) and the t i are terms. Definition 3 (DL-SG knowledge bases and queries). A DL-SG knowledge base is an ordered pair K = (T, A) where T is a primitive TBox and A is an unrestricted ABox. A query is an unrestricted ABox. We note V(K), N (K), R i (K), X (K), T (K) the sets of names, individual names, role names, variables and terms contained in a KB K. An interpretation is an ordered pair I = (∆ I ,. I) where ∆ I is a non-empty set called the interpretation domain, and the interpretation function. I maps each individual name n ∈ N to an element n I of ∆ I , and each role name r of arity k of R k to a subset r I of (∆ I) k (a concept name is mapped to a subset of ∆ I , and ⊥ I = ∅). Definition 4 (Model of a primitive TBox). Let T be a primitive TBox. An interpretation I is a model of T iff for every R R of T , R I ⊆ R I. Definition 5 (Model of an unrestricted ABox). Let A be an unrestricted ABox. An interpretation I is a model of A iff there is a mapping µ : T (A) → ∆ I (called a proof of A in I) such that (i) ∀n ∈ N (A), µ(n) = n I ; and (ii) ∀r(t 1 ,. .. , t k) ∈ A, (µ(t 1),. .. , µ(t k)) ∈ r I. An unrestricted ABox is indeed the linear encoding, with the same semantics, of a positive, conjunctive, existential FOL formula without function symbols, while the TBox encodes implications of form ∀x 1. .. ∀x k (r(x 1 ,. .. , x k) → r (x 1 ,. .. , x k)). A primitive TBox has the same semantics as a CG support, while an unrestricted ABox has the same semantics as a simple CG. This is why the soundness and completeness results presented in this paper can be stated as a direct translation of the CG versions in which they have been proven. Note that (T, A) can also be seen as a relational database by freezing its variables. An interpretation is a model of a KB (T, A) iff it is a model of T and A.
. This paper presents graph operations for processing conceptualgraph rules in forward chaining a... more . This paper presents graph operations for processing conceptualgraph rules in forward chaining and backward chaining. In both casesthe operations provide sound and complete procedures with respect tofirst-order logic deduction. First we present our framework: simple conceptualgraphs, rules as couples of lambda-abstractions, knowledge base,logical semantics. Next we focus on forward chaining. In particular, usingthe notion of redundancy, we exactly characterize
International Joint Conference on Artificial Intelligence, 2009
In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason-... more In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason- ing tasks (as deduction) non-decidable. These rules have the same logical form as TGD (tuple- generating dependencies) in databases and as con- ceptual graph rules. We extend known decidable cases by combining backward and forward chain- ing schemes, in association with a graph that cap- tures exactly
. This paper focuses on two aspects of piece resolution in backwardchaining for conceptual graph ... more . This paper focuses on two aspects of piece resolution in backwardchaining for conceptual graph rules [13]. First, as conceptual graphsadmit a first-order logic interpretation, inferences can be proven by classicaltheorem provers. Nevertheless, they do not use the notion of piece,which is a graph notion. So we define piece resolution over a class offirst-order logical formulae: the logical rules. An
ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des base... more ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des bases de connaissances. Le modèle des graphes conceptuels est un modèle de représentation des connaissances de la famille des réseaux sémantiques, fondé sur la théorie des graphes et sur la logique du premier ordre. Nous proposons une solution pour valider sémantiquement une base de connaissances composée de graphes conceptuels. La validation sémantique d'une base de connaissance consiste à confronter ses connaissances à des contraintes certifiées fiables. Nous proposons d'utiliser des contraintes descriptives, exprimées sous forme de graphes conceptuels, qui permettent de poser des conditions sur la représentation de certaines connaissance dans la base. Ces contraintes introduisent une notion de cardinalités, et sont soit minimales, soit maximales. Elles permettent respectivement d'exprimer "si A, alors au moins ou au plus n fois B". La satisfaction de ces contraintes par une base de connaissances repose sur l'utilisation de l'opération de base du modèle des graphes conceptuels : la projection.
Abstract. In this paper we will discuss two different translations between RDF (Resource Descript... more Abstract. In this paper we will discuss two different translations between RDF (Resource Description Format) and Conceptual Graphs (CGs). These translations will allow tools like Cogui and Cogitant to be able to import and export RDF(S) documents. The first translation is sound and complete from a reasoning view point but is not visual nor a representation in the spirit of Conceptual Graphs (CGs). The second translation has the advantage of being natural and fully ex-ploiting the CG features, but, on the other hand it does not apply to the whole RDF(S). We aim this paper as a preliminary report of ongoing work looking in detail at different pro and the cons of each approach. 1 Introduction and motivation
We consider positive rules in which the conclusion may contain existentially quantified variables... more We consider positive rules in which the conclusion may contain existentially quantified variables, which makes reasoning tasks (such as conjunctive query answering or entailment) undecidable. These rules, called 89-rules, have the same logical form as tuple-generating dependencies in databases and as conceptual graph rules. The aim of this paper is to provide a clearer picture of the frontier between decidability and non-decidability of reasoning with these rules. Previous known decidable classes were based on forward chaining. On the one hand we extend these classes, on the other hand we introduce decidable classes based on backward chaining. A side result is the definition of a backward mechanism that takes the complex structure of 89-rule conclusions into account. We classify all known decidable classes by inclusion. Then, we study the question of whether the union of two decidable classes remains decidable and show that the answer is negative, except for one class and a still op...
This paper reports a collective reflection led in our team about conceptual graph benchmarks. We ... more This paper reports a collective reflection led in our team about conceptual graph benchmarks. We tackle four issues for which agreement should be obtained before benchmarks can be built: what are the fragments of CGs considered? How is information exchanged? What are the problems to be solved? What kinds of tool properties are eval- uated by the benchmarks? We define a basic building block built upon simple conceptual graphs. Finally we propose to provide a first bench- mark adapted from an industrial case study. This benchmark is composed on very simple structures and should allow to focus on interoperability issues.
The research works on knowledge validation aim at enhancing the quality of knowledge bases. The c... more The research works on knowledge validation aim at enhancing the quality of knowledge bases. The conceptual graph model is a knowledge representation model which belongs to the family of the semantic networks. We give a solution to validate semantically a knowledge base expressed in terms of conceptual graphs. The semantic validation of a knowledge base consists in checking that the
This paper reports a collective reflection led in our team about conceptual graph benchmarks. We ... more This paper reports a collective reflection led in our team about conceptual graph benchmarks. We tackle four issues for which agreement should be obtained before benchmarks can be built: what are the fragments of CGs considered? How is information exchanged? What are the problems to be solved? What kinds of tool properties are evaluated by the benchmarks? We define a basic building block built upon simple conceptual graphs. Finally we propose to provide a first benchmark adapted from an industrial case study. This benchmark is composed on very simple structures and should allow to focus on interoperability issues.
Abstract. In this paper we will discuss two different translations between RDF (Resource Descript... more Abstract. In this paper we will discuss two different translations between RDF (Resource Description Format) and Conceptual Graphs (CGs). These translations will allow tools like Cogui and Cogitant to be able to import and export RDF(S) documents. The first translation is sound and ...
Conceptual Graphs offer an attractive and intuitive formalism for knowledge representation in Art... more Conceptual Graphs offer an attractive and intuitive formalism for knowledge representation in Artificial Intelligence. The formalism calls for efficient systems of reasoning. Projection is one such tool for a language limited to conjunction and existential quantification (Simple Conceptual Graphs). Projection is very efficient for certain classes of Conceptual Graphs and offers an original approach to deduction: the perspective of graph matching. The aim of this paper is twofold: Propose an efficient analytic deduction system that combines analytic tableaux with projection for a language of Conceptual Graphs extended to all non functional First-Order Logic formulae and compare this method with the one introduced in [1] for Simple Conceptual Graph rules.
Simple conceptual graphs can be seen as a very basic description logic, allowing however for answ... more Simple conceptual graphs can be seen as a very basic description logic, allowing however for answering conjunctive queries. In the first part of this paper, we translate some results obtained for conceptual graph rules of form "if A then B" into an equivalent DL-based formalism. Then we show that, our algorithms can automatically decide in some cases whether a given DL has the FOL-reducibility property, provided that the semantics of its constructors can be expressed by rules. 2 DL-SG: conjunctive queries, but lite TBox ... 2.1 DL-SG syntax and semantics A vocabulary V is the union of pairwise disjoint sets N , R 1 ,. .. , R k where N contains individual names and R i contains role names of arity i. Role names of arity 1 are called concept names (C = R 1). The set of concept names contains a distinguished element, ⊥ (the absurd concept name). We also consider a set X of variables, disjoint from names of V. The set T = N ∪ X is the set of terms. Definition 1 (Primitive TBox). A primitive TBox is a set of inclusion assertions of form R R where R and R = ⊥ are role names with the same arity. Definition 2 (Unrestricted ABox). An unrestricted ABox is a set of membership assertions of form r(t 1 ,. .. , t p) where r is a role name of arity p (i.e. a concept name if p = 1) and the t i are terms. Definition 3 (DL-SG knowledge bases and queries). A DL-SG knowledge base is an ordered pair K = (T, A) where T is a primitive TBox and A is an unrestricted ABox. A query is an unrestricted ABox. We note V(K), N (K), R i (K), X (K), T (K) the sets of names, individual names, role names, variables and terms contained in a KB K. An interpretation is an ordered pair I = (∆ I ,. I) where ∆ I is a non-empty set called the interpretation domain, and the interpretation function. I maps each individual name n ∈ N to an element n I of ∆ I , and each role name r of arity k of R k to a subset r I of (∆ I) k (a concept name is mapped to a subset of ∆ I , and ⊥ I = ∅). Definition 4 (Model of a primitive TBox). Let T be a primitive TBox. An interpretation I is a model of T iff for every R R of T , R I ⊆ R I. Definition 5 (Model of an unrestricted ABox). Let A be an unrestricted ABox. An interpretation I is a model of A iff there is a mapping µ : T (A) → ∆ I (called a proof of A in I) such that (i) ∀n ∈ N (A), µ(n) = n I ; and (ii) ∀r(t 1 ,. .. , t k) ∈ A, (µ(t 1),. .. , µ(t k)) ∈ r I. An unrestricted ABox is indeed the linear encoding, with the same semantics, of a positive, conjunctive, existential FOL formula without function symbols, while the TBox encodes implications of form ∀x 1. .. ∀x k (r(x 1 ,. .. , x k) → r (x 1 ,. .. , x k)). A primitive TBox has the same semantics as a CG support, while an unrestricted ABox has the same semantics as a simple CG. This is why the soundness and completeness results presented in this paper can be stated as a direct translation of the CG versions in which they have been proven. Note that (T, A) can also be seen as a relational database by freezing its variables. An interpretation is a model of a KB (T, A) iff it is a model of T and A.
Proceedings of the 6th International Conference on Conceptual Structures Theory Tools and Applications, 1998
... Our research group considers the CG model [16] as a declarative model where knowledge is sole... more ... Our research group considers the CG model [16] as a declarative model where knowledge is solely represented by labeled graphs and reasoning is can be done by labeled graphs operations [3]. In a first stage, such a model, the "simple conceptual graph" (SCG) model has ...
ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des base... more ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des bases de connaissances. Le modèle des graphes conceptuels est un modèle de représentation des connaissances de la famille des réseaux sémantiques, fondé sur la théorie des graphes et sur la logique du premier ordre. Nous proposons une solution pour valider sémantiquement une base de connaissances composée de graphes conceptuels. La validation sémantique d'une base de connaissance consiste à confronter ses connaissances à des contraintes certifiées fiables. Nous proposons d'utiliser des contraintes descriptives, exprimées sous forme de graphes conceptuels, qui permettent de poser des conditions sur la représentation de certaines connaissance dans la base. Ces contraintes introduisent une notion de cardinalités, et sont soit minimales, soit maximales. Elles permettent respectivement d'exprimer "si A, alors au moins ou au plus n fois B". La satisfaction de ces contraintes par une base de connaissances repose sur l'utilisation de l'opération de base du modèle des graphes conceptuels : la projection.
In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason-... more In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason- ing tasks (as deduction) non-decidable. These rules have the same logical form as TGD (tuple- generating dependencies) in databases and as con- ceptual graph rules. We extend known decidable cases by combining backward and forward chain- ing schemes, in association with a graph that cap- tures exactly the notion of dependency between rules. Finally, we draw a map of known decidable cases, including an extension obtained by combin- ing our approach with very recent results on TGD.
We study the properties of semantic consequence in a particular subset of first-order logic with ... more We study the properties of semantic consequence in a particular subset of first-order logic with equality and no function symbols, under the unique name assumption. Formulas in this subset of logic are rules of form $\forall \vec x (H \rightarrow \exists \vec y C) where the hypothesis $H$ and the conclusion $C$ are conjunctions of atoms (possibly with equality), $\vec x$ contains the variables in $H$ and $\vec y$ the variables in $C$ that are not in $H$. This subset is particularly expressive since it can encode a universal Turing machine, at the cost of decidability of reasoning. We propose new decidable subclasses of this problem, by combining restrictions on both the structure of the rules themselves and the structure of the interactions between rules, encoded in the graph of rule dependencies. The most general decidable subclass presented here is based on a mixed forward/backward chaining algorithm. Finally, we relate our rules to other notions (tuple-generating dependencies in ...
Simple conceptual graphs can be seen as a very basic de- scription logic, allowing however for an... more Simple conceptual graphs can be seen as a very basic de- scription logic, allowing however for answering conjunctive queries. In the rst part of this paper, we translate some results obtained for con- ceptual graph rules of form \if A then B" into an equivalent DL-based formalism. Then we show that, our algorithms can automatically decide in some cases whether
Simple conceptual graphs can be seen as a very basic description logic, allowing however for answ... more Simple conceptual graphs can be seen as a very basic description logic, allowing however for answering conjunctive queries. In the first part of this paper, we translate some results obtained for conceptual graph rules of form "if A then B" into an equivalent DL-based formalism. Then we show that, our algorithms can automatically decide in some cases whether a given DL has the FOL-reducibility property, provided that the semantics of its constructors can be expressed by rules. 2 DL-SG: conjunctive queries, but lite TBox ... 2.1 DL-SG syntax and semantics A vocabulary V is the union of pairwise disjoint sets N , R 1 ,. .. , R k where N contains individual names and R i contains role names of arity i. Role names of arity 1 are called concept names (C = R 1). The set of concept names contains a distinguished element, ⊥ (the absurd concept name). We also consider a set X of variables, disjoint from names of V. The set T = N ∪ X is the set of terms. Definition 1 (Primitive TBox). A primitive TBox is a set of inclusion assertions of form R R where R and R = ⊥ are role names with the same arity. Definition 2 (Unrestricted ABox). An unrestricted ABox is a set of membership assertions of form r(t 1 ,. .. , t p) where r is a role name of arity p (i.e. a concept name if p = 1) and the t i are terms. Definition 3 (DL-SG knowledge bases and queries). A DL-SG knowledge base is an ordered pair K = (T, A) where T is a primitive TBox and A is an unrestricted ABox. A query is an unrestricted ABox. We note V(K), N (K), R i (K), X (K), T (K) the sets of names, individual names, role names, variables and terms contained in a KB K. An interpretation is an ordered pair I = (∆ I ,. I) where ∆ I is a non-empty set called the interpretation domain, and the interpretation function. I maps each individual name n ∈ N to an element n I of ∆ I , and each role name r of arity k of R k to a subset r I of (∆ I) k (a concept name is mapped to a subset of ∆ I , and ⊥ I = ∅). Definition 4 (Model of a primitive TBox). Let T be a primitive TBox. An interpretation I is a model of T iff for every R R of T , R I ⊆ R I. Definition 5 (Model of an unrestricted ABox). Let A be an unrestricted ABox. An interpretation I is a model of A iff there is a mapping µ : T (A) → ∆ I (called a proof of A in I) such that (i) ∀n ∈ N (A), µ(n) = n I ; and (ii) ∀r(t 1 ,. .. , t k) ∈ A, (µ(t 1),. .. , µ(t k)) ∈ r I. An unrestricted ABox is indeed the linear encoding, with the same semantics, of a positive, conjunctive, existential FOL formula without function symbols, while the TBox encodes implications of form ∀x 1. .. ∀x k (r(x 1 ,. .. , x k) → r (x 1 ,. .. , x k)). A primitive TBox has the same semantics as a CG support, while an unrestricted ABox has the same semantics as a simple CG. This is why the soundness and completeness results presented in this paper can be stated as a direct translation of the CG versions in which they have been proven. Note that (T, A) can also be seen as a relational database by freezing its variables. An interpretation is a model of a KB (T, A) iff it is a model of T and A.
. This paper presents graph operations for processing conceptualgraph rules in forward chaining a... more . This paper presents graph operations for processing conceptualgraph rules in forward chaining and backward chaining. In both casesthe operations provide sound and complete procedures with respect tofirst-order logic deduction. First we present our framework: simple conceptualgraphs, rules as couples of lambda-abstractions, knowledge base,logical semantics. Next we focus on forward chaining. In particular, usingthe notion of redundancy, we exactly characterize
International Joint Conference on Artificial Intelligence, 2009
In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason-... more In ∀∃-rules, the conclusion may contain existen- tially quantified variables, which makes reason- ing tasks (as deduction) non-decidable. These rules have the same logical form as TGD (tuple- generating dependencies) in databases and as con- ceptual graph rules. We extend known decidable cases by combining backward and forward chain- ing schemes, in association with a graph that cap- tures exactly
. This paper focuses on two aspects of piece resolution in backwardchaining for conceptual graph ... more . This paper focuses on two aspects of piece resolution in backwardchaining for conceptual graph rules [13]. First, as conceptual graphsadmit a first-order logic interpretation, inferences can be proven by classicaltheorem provers. Nevertheless, they do not use the notion of piece,which is a graph notion. So we define piece resolution over a class offirst-order logical formulae: the logical rules. An
ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des base... more ABSTRACT Les travaux menés en validation des connaissances visent à améliorer la qualité des bases de connaissances. Le modèle des graphes conceptuels est un modèle de représentation des connaissances de la famille des réseaux sémantiques, fondé sur la théorie des graphes et sur la logique du premier ordre. Nous proposons une solution pour valider sémantiquement une base de connaissances composée de graphes conceptuels. La validation sémantique d'une base de connaissance consiste à confronter ses connaissances à des contraintes certifiées fiables. Nous proposons d'utiliser des contraintes descriptives, exprimées sous forme de graphes conceptuels, qui permettent de poser des conditions sur la représentation de certaines connaissance dans la base. Ces contraintes introduisent une notion de cardinalités, et sont soit minimales, soit maximales. Elles permettent respectivement d'exprimer "si A, alors au moins ou au plus n fois B". La satisfaction de ces contraintes par une base de connaissances repose sur l'utilisation de l'opération de base du modèle des graphes conceptuels : la projection.
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Papers by Eric Salvat