A programme of general semantics

In this paper, we would like to describe two logical systems — Tichy's transparent intensional logic and Girard's linear logic. Transparent intensional logic is a method of logical analysis of natural language, which represents expressive system, independent of chosen source language. Our research vision is to connect this method with linear logic. In future research, this connection would allow us to apply Ludics theory principles (which is the extension of the linear logic) to natural language sentences, which puts them in a logical time and space.

We introduce a new theory of concepts conceived as structured abstract entities. The theory is based on the key notion of Transparent Intensional Logic (TIL), known as TIL construction. The rich procedural semantics of TIL makes it possible to explicitly analyze all the semantically salient features of natural language expressions. We illustrate how to make use of TIL theory of concepts in distinguishing analytical and empirical concepts, and particular kinds of necessities. We also deal with a rigorous specification of requisite relations between intensions such as properties. Finally, ontology is characterised as a relatively stable part of the system that should play an integrating role. We show how to make use of TIL rich theory in specification of the content of ontologies in a multi-agent system.

This paper describes the design of a knowledge representation and reasoning system, named Dolphin, which is based on higher-order temporal Transparent Intensional Logic (TIL). An intelligent agent (NAM), that is able to read newspaper headlines from specialized internet server and allows users to ask questions about various world situations is chosen to demonstrate Dolphin features. Temporal aspects play an essential role in natural language therefore we present how this phenomenon is handled in the system. Reasoning capabilities of the agent are divided into three individual strategies and described in the text. As a result we compare NAM answers to one of the most used search engines nowadays.

Formal semantics of natural language: Edward L. Keenan (ed.), Papers from a colloquium sponsored by the King's College Research Centre, Cambridge, England. Cambridge University Press, London, 1975. xiii, 475 pp. £12.50.

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions (mappings). Instead they are higher-order, fine-grained structures. I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed $$\lambda $$ -calculus, whose $$\lambda $$ -terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context.

In the paper we show that sentences differing only in topic-focus articulation have different logical structures, and thus they also have different truth-conditions. Our analysis is based on the procedural semantics of Transparent Intensional Logic (TIL) assigning to sentences hyperpropositions as their structured meanings. We analyse the phenomena of presupposition connected with a topic and allegation triggered by a focus of a sentence so that relevant consequences can be formally derived.

John Venn and logical theory

In natural language we meet sentences of quite different grammatical and logical structure. Sentential logic and the logic of quantifiers investigate some “basic structures” of language expressions. In the last few decades logicians have created a lot of formal systems to extend the expressive power and potential of formal languages in accordance with the multiplicity of forms in the natural language. In the main it has been by constructing ideal languages, i.e. under assumptions which are not fulfilled by natural language or by real language communication. Many problems arise if we try to apply logical analysis to philosophy or other sciences which use natural language.

Abstract

In this paper, we offer one possible way to bridge the gap existing between the lexical and logical semantic analysis of natural language expressions. We look for a link that would allow us to perform a more adequate and integrated semantic analysis of natural language expressions. The solution is to combine the descriptions of lexical units as they are developed within the area of lexical semantics (e.g. WordNet) with logical analysis of sentence meanings worked out within the Transparent Intensional Logic framework.

A system of tensed intensional logic excluding iterations of intensions is introduced. Instead of using the type symbols (for ‘sense’), extensional and intensional functor types are distinguished. A peculiarity of the semantics is the general acceptance of value-gaps (including truth-value-gaps): the possible semantic values (extensions) of extensional functors are partial functions. Some advantages of the system (relatively to R. Montague's intensional logic) are briefly indicated. Also, applications for modelling natural languages are illustrated by examples.

PREFACE, ABBREVIATIONS, 1. THE NEED FOR A LOGICAL CALCULUS FOR THE THEORY OF SINN AND BEDEUTUNG, Introduction, Frege's Project: Logicism and the Notion of Begriffsschrift, The Theory of Sinn and Bedeutung, The Limitations of the Begriffsschrift, Filling the Gap, 2. THE LOGIC OF THE GRUNDGESETZE, Logical Language and the Content of Logic, Functionality and Predication, Quantifiers and Gothic Letters, Roman Letters: An Alternative Notation for Generality, Value-Ranges and Extensions of Concepts, The Syntactic Rules of the Begriffsschrift, The Axiomatization of Frege's System, Responses to the Paradox, 3. SINNE AND GEDANKEN, The Nature of Sinne Generally, The Sinne of Incomplete Expressions and the Composition of Gedanken, Context Principle, Priority Thesis, and Multiple Analyses: Challenges to Compositionality, The Identity Conditions of Sinne and Gedanken, 4. CHURCH'S LOGIC OF SENSE AND DENOTATION, Overview, The Method of Transparent Intensional Logic, Alternatives (0), (1) and (2) and Synonymous Isomorphism, The Formulation of the Systems, Problems in Church's Logic of Sense and Denotation, The UnFregean Elements of Church's Logic of Sense and Denotation, 5. A LOGICAL CALCULUS FOR THE THEORY OF SINN AND BEDEUTUNG, Basic Features, Names and Variables for Sinne, The New Constants of the Expanded Language, Syntactic Rules of the Expanded Language, Axioms and Inference Rules of the Expanded Calculi, Inferences Involving Propositional Attitudes and Quantifying In, Difficulties with the Expanded Calculi, 6. COMPARISON WITH RUSSELL AND OTHER THINKERS, Solatium miseris, socios habuisse malorum., Russell's Ontology of Propositions, Russell and the Principles of Mathematics Appendix B Paradox, Frege and the Principles of Mathematics Appendix B Paradox, Lessons Learned from Russell, Other Systems of Intensional Logic, 7. POSSIBLE REVISIONS TO FREGE'S PHILOSOPHY, Adequate versus Ad Hoc Solutions, A Cantorian Analysis of the Difficulties, Dropping Classes and/or Concepts, Reducing the Number of Sinne and Gedanken, Ramification as a Solution to the Paradoxes, The Justification of Ramification, Conclusion, APPENDIX: SUMMARY OF DEFINITIONS, AXIOMS AND INFERENCE RULES, BIBLIOGRAPHY, INDEX

This paper aims to formally define a concept of interpretability according to natural language of a logical theory, and show advances for demonstrating that the logic system called Compensatory Fuzzy Logic is interpretable. A logical theory is interpretable according to natural language if the calculus based upon the elements of this logical theory can be understood in natural language and vice versa. We present conditions necessary for a logical theory to be called interpretable, especially Compensatory Fuzzy Logic.

Montague grammarians claim that the logical analysis of language sketched in standard textbooks of first order logic is too coarse to be appropriate to such natural languages as English. In the following we shall defend the opposite view - at least as far as a very narrow fragment of English is concerned, traditional logical analysis is perfectly adequate provided we are ready to pay the price of abandoning classical logic in favour of logics containing a sufficiently rich stock of logical constants. Within the framework of Casari's comparative logic, we shall outline a model of a restricted fragment of English. We shall address such issues as the construction of complex noun phrases, the distinction between gradable and vague adjectives, the structure of comparative sentences and of antonym adjectival pairs

Grammatical elements such as determiners, conjunctions or pronouns are very evenly dispersed across natural language data. By contrast, the uses of lexical elements have a stronger tendency to occur in bursts that are interspersed by long lulls. This paper considers two alternative explanations for this difference. First, it could be hypothesised that the more even distribution of grammatical elements is merely an effect of an element's high text frequency. Alternatively, it could be argued that a more even distribution is a symptom of greater generality in meaning. In order to assess the impact of both frequency and semantic generality, we conducted a corpus-based study that contrasts lexical and grammatical elements in Present-Day English. Our results suggest that evenness of dispersion is chiefly an effect of high frequency.