Anselm of Cantorbery wrote Proslogion, where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by absurd, (...) that “quod non posit cogitare non esse” by using the hypothesis: “to think in re” is taller than “to think in solo intelectu”. We discuss this relation and the difference between the meanings of the elementary predicates ‘to be in re’, ‘to be in intellectu’ and ‘to be in solo intellectu’. We propose a new logical approach of this ‘Unum argumentum’ of Anselm by using Curry’s Combinatory Logic. Indeed, Combinatory Logic is an abstract applicative formalism of operators applied to operands; in this formalism, the predicates, viewed as specific operators, can be composed and can be transformed, by an intrinsic way, into more complex predicates, by means of abstract operators, called “combinators”, studied by Combinatory Logic. We show that this formalism is a logical frame where it becomes possible to discuss and to formulate cognitive representations of the meanings of predicates used inside of the ‘Unum argumentum’ and to explain how the argument runs. (shrink)

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 , using the applicative formalism, functional types of categorial grammars and combinatory logic . In the enunciative theory and following , an utterance can be decomposed into two components: a modus and a (...) dictum . In GRACE, the modus is a complex operator applied to a proposition 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. (shrink)

From a logical viewpoint, object is never defined, even by a negative definition. This paper is a theoretical contribution about object using a new constructivist logical approach called Logic of Determination of Objects founded on a basic operation, called determination. This new logic takes into account cognitive problems such as the inheritance of properties by non typical occurrences or by indeterminate atypical objects in opposition to prototypes that are typical completely determinate objects. We show how extensional classes, intensions, more and (...) less determined objects, more or less typical representatives of a concept and prototypes are defined and organized, using a determination operation that constructs a class of indeterminate objects from an object representation of a concept called typical object. (shrink)