Pdf conceptual graphs and first order logic iadh ounis. Conceptual graphs and dataflow graphs, their dynamic variety, provide means to reason over propositions in first order logics. Abstract we study sowas conceptual graphs cgs with both existential and universal quantifiers. Conceptual structures cs theory is a logicbased knowledge representation formalism. Types of formal mathematical logic propositional logic propositions are interpreted as true or false infer truth of new propositions first order logic contains predicates, quantifiers and variables e. They have the full power of first order logic and can represent model and higher order logic. But many of the issues concerning the use of conceptual graphs as a metalanguage have not been worked out in detail. For the first formal logic, aristotle developed a stylized or controlled version of natural language nl. Probably the most important one is sowas system of conceptual graphs from which sowa claims that they have at least the expressiveness of first order predicate logic fopl. Citeseerx document details isaac councill, lee giles, pradeep teregowda. If there is power to the plugs and the plugs are clean, a good spark is. Pdf in the iccs 2000 proceedings we introduced negation to simple concept graphs without generic markers by adding cuts to their definition.
A conceptual graph is a graph or network of two kinds of nodes, concepts and relations. Conceptual graphs, however, do not of themselves capture the. The problem with these structures is that they could never fully express full first order logic. To show that conceptual graphs have the power of firstorder logic, it is. After this a modification of peirces betacalculus is provided, and definitions for mappings. The translation of conceptual graphs to firstorder logic is done according to certain rules. Conceptual graphs and first order logic, the computer journal. In contrast to logicbased systems where semantics and proof theory are important to understand and derive knowledge, in conceptual graph theory two alternative. In the late 1970s, many graph notations were designed to represent firstorder logic or a formallydefined subset findler 1979. We study sowas conceptual graphs cgs with both existential and universal quantifiers. From all these sources we learn that semantic networks have three main attributes. This version of the rules was adapted from a tutorial on existential graphs by peirce 1909. Conceptual structures cs theory is a logic based knowledge representation formalism. Predicate logic is more powerful than propositional logic as it allows for quantification.
Languages and diagrams for logic existential graphs and the conceptual graphs based on them are formally defined, but they follow the long tradition of deriving logical patterns from language patterns. We assume a set can be a set of anything and that the universe can be physical or abstract or any mixture in order to make our universe as general as. In logic, the implication operator determines a generalization hierarchy. A conceptual graph cg is a graph representation for logic based on the.
The logic system of concept graphs with negation and its. To represent logic more concisely, however, the extended syntax supports special contexts and defined quantifiers, which can all be translated to the core structures. We extend and modify sowas original graph derivation system with new rules and prove the soundness and completeness theorem with respect to sowas standard interpretation of cgs into first order logic fol. The metalanguage of conceptual graphs is used to capture requirements expressed in various conventional requirements development notations. Conceptual completeness for firstorder intuitionistic logic. If there is gas in the engine and a good spark, the engine runs.
A conceptual graph cg is a formalism for knowledge representation. This peirce logic is developed by sowa in the same. The semantic tableau is a logic diagram, which shows a decision procedure for sentential and related logics, and a proof procedure for formulas of firstorder logic. In the late 1970s, many graph notations were designed to represent first order logic or a formallydefined subset. Pdf concept graphs with cuts as diagrammatic first order logic. Pdf accepted manuscript requires a pdf viewer such as gsview. Conceptual graphs and first order logic the computer. A first order sentence s in the logic of graphs is said to define a graph g if g is the only graph that models s. Existential graphs egs are a simple, readable, and expressive graphic notation for logic. Conceptual graphs in this paper, we propose a simple and well established semantics for conceptual graphs.
Castiglione, 59, 00142 rome, italy 2department of computing science, university of glasgow, glasgow g12 8qq, uk email. Conceptual graphs and first order logic request pdf. For these graphs, a settheoretical semantics is presented. In addition to that, we thoroughly compare conceptual graphs with first order predicate logic fopl. The standardos main sections prescribe a set of syntactic and. The first definition is, a conceptual graph g is a bipartite graph that. Concepts are mathematized using formal concept analysis fca, while an approach to the formalization of judgements and conclusions is conceptual graphs, based on peirces existential graphs. Conceptual graphs cgs combine a logical foundation based on egs with features of the semantic networks used in artificial intelligence and computational linguistics. The conceptual graph formalism is a good candidate for the representation of corporate knowledge, and for the development of knowledge management systems. Syntax of firstorder logic semantics of firstorder logic. Jan 01, 2000 conceptual graphs and first order logic conceptual graphs and first order logic gianni amati, iadh ounis 20000101 00. Every graph may be defined by at least one sentence. First, it is about fuzzy conceptual graphs and their logic programming foundations, as a graphbased order sorted fuzzy set logic programming language for automated reasoning with fuzzy object attributes and types.
Conceptual graphs and first order logic, the computer. Sowa developed a version of conceptual graphs cgs as an intermediate language for mapping natural language questions and assertions to a relational database. Pdf concept graphs and predicate logic researchgate. The rectangles are called concepts, and the circles. It is cgs inference capability that can assist in determining this knowledge. From a computational viewpoint, the graph homomorphism notion was recognized in the 1990s as a central notion, and complexity results and efficient algorithms have. The aim of this paper is to extend this approach of cuts to simple concept graphs with generic markers. If there is gas in the tank and the fuel line is okay, then there is gas in the engine. They have traditionally had a strong emphasis on twodimensional graphical representations, but there are conventional serializations, one linear form much comparable with n3, and one cg interchange format cgif which is more. Castiglione, 59, 00142 rome, italy 2 department of computing science, university of glasgow, glasgow g12 8qq, uk email. Write a prolog program to calculate the sum of two numbers. Conceptual graphs and firstorder logic springerlink.
The most basic definitions in a conceptual graphs are the concepts and. An introduction to conceptual graphs 7 6 inference inference in conceptual graphs theory is based upon the existential graphs logic of charles sanders peirce6. Saying it with pictures institute for logic, language and computation. Among these, in the conceptual graph, to represent a nested structure in predicate logic. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things.
Conceptual graphs and first order logic gianni amati1. Artificial intelligence guidelines and practical list pdf. Grammars firstorder logic learning a theory and new. Firstorder logic propositional logic only deals with facts, statements that may or may not be true of the world, e. Conceptual graphs and fuzzy logic a fusion for representing. The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. To put it in a nutshell, conceptual graphs cgs are a logic language used for describing closed worlds of logic. They have the full power of firstorder logic and can represent model and higherorder logic. Network representation semantic networks and conceptual graphs procedural representation this will be included in the section on expert systems. Conceptual graphs and first order logic the computer journal. The nodes in the graph represent objects or concepts and. To show that conceptual graphs have the power of firstorder logic, it is necessary to have a mapping between both formalisms.
Logical representation first order predicate calculus with implementation in prolog. Once translated into conceptual graphs, the set of requirements is analyzed in order to find the most. Practice questions on propositional and first order logic 1. Write a prolog program to implement maxx, y, m so that m is the maximum of two numbers x and y. From existential graphs to conceptual graphs john f. A network representation of firstorder logic that uses token. The first book on cgs applied them to a wide range of topics in artificial intelligence, computer science, and. Formal semantics how do we decide if a rstorder formula is true. Complex information or even argumentation can often better be conveyed by diagrams than by any linear notions, like language or formulas. Conceptual graphs introduction to ontologies and semantic. This model theoretic semantics is an alternative to previous approaches, where a game theoretical semantics has been suggested. In addition to that, we thoroughly compare conceptual graphs with first order.
A multiple viewed approach to software requirements. Logic interpretation sowa proposes sowa, 2000 to associate with every cg a well formed formula, based of the. Conceptual graphs to allow more powerful analysis of the dependencies of a given system. We extend and modify sowas original graph derivation system with new rules and prove the. Firstorder logic in cognition may be skeptical, because people have a hard time reasoning logically. Existential graphs and the conceptual graphs based on them are formally defined, but they follow the long tradition of deriving logical patterns from language patterns. Conceptual graphs have a direct translation into natural language. Concept graphs with cuts as diagrammatic first order logic. This method, which we term analytic tableaux, is a variant of the semantic tableaux of beth 1, or of methods of hintikka 1. Logical, philosophical, and computational foundations john e sowa pacific grove, ca. Yet peirce felt that the predicate notation for logic was unduly complex.
Sowa 1976 developed a version of conceptual graphs cgs as an intermediate language for mapping natural language questions and assertions to a relational database. Sound and complete for firstorder definite clauses proof similar to propositional proof. In the late 1970s, many graph notations were designed to represent first order logic or a formallydefined subset findler 1979. Firstorder logic in knowledge graphs sciencedirect. The common logic standard is not just for conceptual graphs. This formalism is based on semantic networks, but it has direct translation to the language of first order predicate logic, from which it takes its semantics. Sowa introduced a hyperconcept named proposition and succeeded. Conceptual graphs, metamodeling, and notation of concepts. Sowa used them to represent the conceptual schemas used in database systems. They express meaning in a form that is logically precise, humanly readable, and computationally tractable.
Conceptual analysis conceptual theory language method 1. Conceptual graphs cg is a logical formalism that includes classes, relations, individuals and quantifiers. Conceptual graphs and first order logic conceptual graphs and first order logic gianni amati, iadh ounis 20000101 00. The importance of logic is in expressive representation, not. Conceptual graphs consist of a formal language to access knowledge and meaning. Another signi cant new concept in rstorder logic is quanti cation. Conceptual graphs cgs are a system of logic based on the existential graphs of charles sanders peirce and the semantic networks of artificial intelligence. Diagrammatic reasoning, first order logic, concept graphs with cuts, conceptual graphs 1 introduction and overview in human reasoning, diagrams play an essential role. Conceptual graphs and firstorder logic open research online.
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