An Occurrence Description Logic Badie, Farshad; Gotzsche, Hans
Logical Investigations,
06/2022, Volume:
28, Issue:
1
Journal Article
Peer reviewed
Open access
Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed ...Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in Deviational Syntactic Structures under the label ‘EFA(X)3’ (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article—based on our OccL-based definitions of the concepts of strong implication and occurrence value as well as of the logical concept Identical Occurrence Constructor (IDOC) that is the most fundamental logical concept in our formalism—we will model Occurrence Description Logic (ODL). Accordingly, we will formally-logically analyse ‘occurrence(s) of symbol(s)’ within descriptions of the world in ODL. In addition, we will analyse and assess the logical concepts of occurrence and occurrence priority in ODL. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic.
La concepción de la lógica y del pragmaticismo de Peirce es casi la de la semántica de teoría de juegos de Hintikka, incluida la idea de jugadores "simulados en nuestra imaginación". Peirce estaba ...interesado por la lógica como teoría de la acción estratégica, habitual, convencional y normativa. Más tarde, Grice erigiría su teoría de la conversación sobre fondo peirceano. Pero la cooperación es una propiedad de los juegos de construcción de modelos y un elemento fundamental del método de Peirce. La construcción de modelos cooperativa conlleva el mismo constructo teórico que el de los juegos semánticos estrictamente competitivos. Ambos tipos de juegos, los semánticos y los de construcción de modelos, constituyen las dos caras de una misma moneda conceptual. Los principios generales que gobiernan las prácticas matemáticas están relacionados con las actividades de construcción de modelos. Peirce's conception of logic and pragmaticism is virtually that of Hintikka's game-theoretical semantics (GTS), including the idea of players "feigned in our makebelieve". Peirce was interested in logic as a theory of normative, conventional, habitual and strategic action. Later Grice erected his theory of conversation on Peircean background. But cooperation is a property of model-building games and an integral part of Peirce's method. Cooperative model-building resorts to the same theoretical construct as the strictly competitive semantic games do. The two kinds of games, the semantic and the model-construction games, are two sides of the same conceptual coin. General principles governing mathematical practices are related to model-building activities.
En un momento de su libro de 1985 Reasoning with Arbitrary Objects, Kit Fine observa y enfatiza tres, en su opinión, importantes diferencias entre objetos-A y funciones de Skolem. El presente ...artículo está dedicado, en particular, a la discusión de una de ellas. Según Fine, existen dependencias entre objetos que no pueden ser representadas propiamente por ninguna función. En lo que sigue, analizaremos esta afirmación desde la perspectiva del lenguaje natural y discutiremos la mejora que parece introducir el uso de objetos arbitrarios frente al de funciones de Skolem en el tratamiento de la dependencia. In 1985, in his book Reasoning with Arbitrary Objects, Kit Fine observed and stressed three, in his opinion, important differences between A-objects and Skolem functions. The present paper rests on one of them. According to Fine, there is some kind of dependence relationship between objects that cannot properly be represented by any function. We will analyze this claim from the perspective of natural language, and discuss the improvement that the use of arbitrary objects seemingly provides over Skolem functions in dealing with dependence.
Los conjuntos Hintikka pueden verse como descripciones parciales de un mundo posible y usarse para construir modelos formales en una lógica modal para la interpretación de las expresiones del ...discurso en el marco de un contexto o una situación concretos. Para ello, definimos los contextos lingüísticos mediante conjuntos Hintikka como un sistema de marcos que permite al hablante/oyente asignar referencia, por ejemplo, a cualquier expresión anafórica de un modo general, tomando el mejor candidato como referente en cada fragmento de discurso para darle una interpretación. Hintikka sets can be viewed as partial descriptions of a possible world and used to construct formal modal models for interpretation of discourse expressions in a concrete context or situation. Linguistic contexts are accordingly defined by means of Hintikka sets as a system of frames that allows the hearer/speaker to assign a reference, for instance, to any anaphoric expression in a general way, picking up the best referential candidate for each fragment of discourse to get its interpretation.
En este artículo describiremos brevemente el sistema que en lógica es conocido como lógica IF (lógica amigable con la independencia) y que fue introducido por Hintikka y Sandu en 1989. Es conocido ...que esta lógica tiene enunciados que son indeterminados. Tras esto, mostraremos cómo resolver la indeterminación de sus enunciados aplicando el teorema Minimax de von Neumann. Este artículo se basa en gran medida en Sevenster y Sandu (2010), Mann, Sandu, y Sevenster (2011), Sandu (2012), Sandu (en prensa), and Barbero and Sandu (en prensa). In this paper we shall shortly describe the system of logic known as IF logic (Independence friendly logic) introduced in Hintikka and Sandu (1989). It is known that this logic has indeterminate sentences. After that we will show how we can resolve the indeterminacy of its sentences by applying von Neumann's Minimax theorem. This paper draws heavily on Sevenster and Sandu (2010), Mann, Sandu, and Sevenster (2011), Sandu (2012), Sandu (forthcoming), and Barbero and Sandu (forthcoming).
In mathematics education, it is often said that mathematical statements are necessarily either true or false. It is also well known that this idea presents a great deal of difficulty for many ...students. Many authors as well as researchers in psychology and mathematics education emphasize the difference between common sense and mathematical logic. In this paper, we provide both epistemological and didactic arguments to reconsider this point of view, taking into account the distinction made in logic between truth and validity on one hand, and syntax and semantics on the other. In the first part, we provide epistemological arguments showing that a central concern for logicians working with a semantic approach has been finding an appropriate distance between common sense and their formal systems. In the second part, we turn from these epistemological considerations to a didactic analysis. Supported by empirical results, we argue for the relevance of the distinction and the relationship between truth and validity in mathematical proof for mathematics education.
