Logic and Sense

Bulletin of the Section of Logic

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two ...

1998

This paper reminds, puts in order, sketches and also initiates some researches from the field of logic and philosophy of language. It lays emphasis on the logical-linguistic and ontological developmental lines originated with Polish researchers. The author discusses two opposite orientations of the former line in the process of formalization of language, called here nominalistic and Platonistic. The paper mentions the author's result (1989; 1991) concerning theoretical equivalence of two axiomatic approaches to language syntax which take into consideration these two different philosophical orientations, respectively. It also introduces certain formal-logical foundations of language semantics, discusses and develops the problem of the syntactic and semantic categorial agreement, i.e. the agreement of the syntactic category of each language expression with the ontological category assigned to the reference of this expression. The author, in particular, gives a solution to this problem for quantifiers.

Contemporary Polish Ontology, 2019

The main purpose of the paper is to outline the formal-logical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a double ontological status. They are understood as either concretes, that is tokens-material, physical objects, or typesclasses of tokens, which are abstract objects. Such a duality is taken into account in the presented logical theory of syntax, semantics and pragmatics. We point to the possibility of building it on two different levels; one which stems from concretes, language tokens of expressions, whereas the other one-from their classes, types conceived as abstract, ideal beings. The aim of this work is not only to outline this theory as taking into account the functional approach to language, with respect to the dual ontological nature of its expressions, but also to show that the logic based on it is ontologically neutral in the sense that it abstracts from accepting some existential assumptions, related with the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects).

1984

The Philosophical Relevance of the Concept of Meaning – I, 1976

2021

On the proof-theoretic side, logic, roughly speaking, is mainly about the grammar of the language (syntax), and reasoning on this language (consequence relations). On the model-theoretic side, we further provides mathematical structures that evaluates the language (semantic models). Among these, syntax is perhaps the easiest part. What one usually does to specify the syntax is to first fix a set of variablesX , which almost always is chosen to be a countably infinite set, and then define the set of well-formed formulas Fml with variables being in X . Here in this paper we will confine ourselves to only consider language of algebraic nature. ‘is means that our signature for the language would be algebraic, and the only formula-forming rules would be application of function symbols. Syntax in richer context with variable bindings could become much less trivial. ‘e more interesting part of logic in our se‹ing is how to reason with the given language, and how we provide the semantics. F...

Studies in Logic, Grammar and Rhetoric, 2015

The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most general one being: the compatibility of the language syntax with its bi-level semantics: intensional and ex-tensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory of syntax T of any categorial language L generated by the so-called classical categorial grammar, and also on the ground of its extension to the bi-level, intensional and ex-tensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch. S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) – material, concrete objects – and then as a language of wfe-types – abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semantics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of com-positionality.

Proceedings of the 8th conference on Computational linguistics -, 1980

Model theoretic semantics (MTS) has a special attitude to describe semantics, to characterize both artificial and natural languages by pure mathematical tools and some of the basic properties of this attitude are disscussed. The arsenal of MTS equipped here with such tools allowing the investigation at such a level of complexity that approximates the real situations. These tools are developed within the frame of category theory.

Mathematical and Computational Analysis of Natural Language, 1998