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. Conceptual graphs and sweb reflections on web architecture. Conceptual analysis conceptual theory language method 1. Sowa used them to represent the conceptual schemas used in database systems. The conceptual graph formalism is a good candidate for the representation of corporate knowledge, and for the development of knowledge management systems. Conceptual graphs and first order logic, the computer. Conceptual completeness for firstorder intuitionistic logic. After this a modification of peirces betacalculus is provided, and definitions for mappings.
In 1882, he had devel oped his relational graphs, which could express the sentence a. Practice questions on propositional and first order logic 1. Sowa 1976 developed a version of conceptual graphs cgs as an intermediate language for mapping natural language questions and assertions to a relational database. This method, which we term analytic tableaux, is a variant of the semantic tableaux of beth 1, or of methods of hintikka 1. In the late 1970s, many graph notations were designed to represent firstorder logic or a formallydefined subset findler 1979.
From a computational viewpoint, the graph homomorphism notion was recognized in the 1990s as a central notion, and complexity results and efficient algorithms have. Saying it with pictures institute for logic, language and computation. 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. The first book on cgs applied them to a wide range of topics in artificial intelligence, computer science, and. They express meaning in a form that is logically precise, humanly readable, and computationally tractable.
Castiglione, 59, 00142 rome, italy 2 department of computing science, university of glasgow, glasgow g12 8qq, uk email. Conceptual graphs in this paper, we propose a simple and well established semantics for conceptual graphs. Artificial intelligence guidelines and practical list pdf. The nodes in the graph represent objects or concepts and. Sowa developed a version of conceptual graphs cgs as an intermediate language for mapping natural language questions and assertions to a relational database. Logic interpretation sowa proposes sowa, 2000 to associate with every cg a well formed formula, based of the. Predicate logic is more powerful than propositional logic as it allows for quantification. We are only going to look at one logical representation scheme, namely, firstorder predicate logic. Conceptual graphs to allow more powerful analysis of the dependencies of a given system.
A conceptual graph is a graph or network of two kinds of nodes, concepts and relations. Pdf conceptual graphs and first order logic iadh ounis. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The importance of logic is in expressive representation, not. Sound and complete for firstorder definite clauses proof similar to propositional proof. Conceptual graphs introduction to ontologies and semantic. They have the full power of first order logic and can represent model and higher order logic. 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. This version of the rules was adapted from a tutorial on existential graphs by peirce 1909. In addition to that, we thoroughly compare conceptual graphs with first order predicate logic fopl. Conceptual graphs and first order logic gianni amati1. Write a prolog program to implement maxx, y, m so that m is the maximum of two numbers x and y.
Once translated into conceptual graphs, the set of requirements is analyzed in order to find the most. 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 study sowas conceptual graphs cgs with both existential and universal quantifiers. Write a prolog program to calculate the sum of two numbers. There was always something missing in these structures that could be fully captured with the introduction of the conceptual graphs.
A conceptual graph cg is a formalism for knowledge representation. The logic system of concept graphs with negation and its. Syntax of firstorder logic semantics of firstorder logic. We extend and modify sowas original graph derivation system with new rules and prove the. Conceptual graphs and first order logic request pdf. But many of the issues concerning the use of conceptual graphs as a metalanguage have not been worked out in detail. If there is gas in the engine and a good spark, the engine runs. The standardos main sections prescribe a set of syntactic and. Every graph may be defined by at least one sentence. A conceptual graph cg is a graph representation for logic based on the. Existential graphs egs are a simple, readable, and expressive graphic notation for logic.
The most basic definitions in a conceptual graphs are the concepts and. Castiglione, 59, 00142 rome, italy 2department of computing science, university of glasgow, glasgow g12 8qq, uk email. An introduction to conceptual graphs 7 6 inference inference in conceptual graphs theory is based upon the existential graphs logic of charles sanders peirce6. From all these sources we learn that semantic networks have three main attributes. Conceptual graphs cg is a logical formalism that includes classes, relations, individuals and quantifiers. 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. The first definition is, a conceptual graph g is a bipartite graph that. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things.
Logical, philosophical, and computational foundations john e sowa pacific grove, ca. Conceptual graphs and first order logic the computer journal. This peirce logic is developed by sowa in the same. Firstorder logic propositional logic only deals with facts, statements that may or may not be true of the world, e. Yet peirce felt that the predicate notation for logic was unduly complex. For the first formal logic, aristotle developed a stylized or controlled version of natural language nl. Concept graphs with cuts as diagrammatic first order logic. Conceptual graphs and fuzzy logic a fusion for representing. In the late 1970s, many graph notations were designed to represent first order logic or a formallydefined subset findler 1979. 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.
A multiple viewed approach to software requirements. 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. To represent logic more concisely, however, the extended syntax supports special contexts and defined quantifiers, which can all be translated to the core structures. Among these, in the conceptual graph, to represent a nested structure in predicate logic. This model theoretic semantics is an alternative to previous approaches, where a game theoretical semantics has been suggested. In contrast to logicbased systems where semantics and proof theory are important to understand and derive knowledge, in conceptual graph theory two alternative.
Conceptual graphs and first order logic the computer. Conceptual graphs and first order logic, the computer journal. Conceptual graphs, however, do not of themselves capture the. In the late 1970s, many graph notations were designed to represent first order logic or a formallydefined subset. Jan 01, 2000 conceptual graphs and first order logic conceptual graphs and first order logic gianni amati, iadh ounis 20000101 00. 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. Conceptual graphs cgs are a system of logic based on the existential graphs of charles sanders peirce and the semantic networks of artificial intelligence. Conceptual structures cs theory is a logic based knowledge representation formalism.
The aim of this paper is to extend this approach of cuts to simple concept graphs with generic markers. Logical representation first order predicate calculus with implementation in prolog. Conceptual graphs and dataflow graphs, their dynamic variety, provide means to reason over propositions in first order logics. Conceptual structures cs theory is a logicbased knowledge representation formalism. The rectangles are called concepts, and the circles.
To put it in a nutshell, conceptual graphs cgs are a logic language used for describing closed worlds of logic. Complex information or even argumentation can often better be conveyed by diagrams than by any linear notions, like language or formulas. Network representation semantic networks and conceptual graphs procedural representation this will be included in the section on expert systems. Firstorder logic in knowledge graphs sciencedirect. If there is power to the plugs and the plugs are clean, a good spark is. Conceptual graphs have a direct translation into natural language. 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. In the late 1970s, many graph notations were designed to represent firstorder logic or a formallydefined subset. In addition to that, we thoroughly compare conceptual graphs with first order. Pdf concept graphs and predicate logic researchgate. They have the full power of firstorder logic and can represent model and higherorder logic. The problem with these structures is that they could never fully express full first order logic.
Conceptual graphs cgs combine a logical foundation based on egs with features of the semantic networks used in artificial intelligence and computational linguistics. If there is gas in the tank and the fuel line is okay, then there is gas in the engine. 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. The metalanguage of conceptual graphs is used to capture requirements expressed in various conventional requirements development notations. Sowa introduced a hyperconcept named proposition and succeeded. Pdf concept graphs with cuts as diagrammatic first order logic. Firstorder logic in cognition may be skeptical, because people have a hard time reasoning logically.
Formal semantics how do we decide if a rstorder formula is true. Conceptual graphs and firstorder logic open research online. First w e w i l l i n d u c t i v e l y d e f i n e definition 2. 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. Abstract we study sowas conceptual graphs cgs with both existential and universal quantifiers. Conceptual graphs, metamodeling, and notation of concepts. It is cgs inference capability that can assist in determining this knowledge. The common logic standard is not just for conceptual graphs.
The translation of conceptual graphs to firstorder logic is done according to certain rules. To show that conceptual graphs have the power of firstorder logic, it is. For these graphs, a settheoretical semantics is presented. Pdf in the iccs 2000 proceedings we introduced negation to simple concept graphs without generic markers by adding cuts to their definition. Pdf accepted manuscript requires a pdf viewer such as gsview. 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. From existential graphs to conceptual graphs john f. Conceptual graphs consist of a formal language to access knowledge and meaning. To show that conceptual graphs have the power of first order logic, it is necessary to have a mapping between both formalisms. To show that conceptual graphs have the power of firstorder logic, it is necessary to have a mapping between both formalisms. 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 springerlink.