Based on the Eleventh International Conference on General Semantics--"A search for relevance, 1968".

From her first chapter giving a historical sketch of the main ideas to her final chapter surveying the ways in which they have influenced education in America, ...

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and (...) structured objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality. (shrink)

This paper uses an "admissible set semantics" to treat quantification in quantified modal logics. The truth condition for the universal quantifier states that a universally quantified statement (x)A(x) is true at a world w if and only if there is some proposition true at that world that entails every instance of A(x). It is shown that, for any canonical propositional modal logic the corresponding admissible set semantics characterises the quantified version of that modal logic.

The fundamental, irreplaceable exposition of general semantics. In this work Korzybski developed important lines of formulating neglected by subsequent authors. A must-have for the student of general semantics interested in the original formulations of Alfred Korzybski. The sixth edition of Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics includes a new preface by Lance Strate, President of the Institute of General Semantics.

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and (...) truth values, therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (shrink)

Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary first-order formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) (...) of first-order logic, making it decidable. Next, we relate guarded syntax to earlier quantifier restriction strategies for achieving effective axiomatizability in second-order logic – pointing at analogies with ‘persistent’ formulas, which are essentially in the Bounded Fragment of many-sorted first-order logic. Finally, we look at some further unexplored directions, including the systematic use of ‘quasi-models’ as a semantics by itself. (shrink)

In the context of life sciences, we are constantly confronted with information that possesses precise semantic values and appears essentially immersed in a specific evolutionary trend. In such a framework, Nature appears, in Monod’s words, as a tinkerer characterized by the presence of precise principles of self-organization. However, while Monod was obliged to incorporate his brilliant intuitions into the framework of first-order cybernetics and a theory of information with an exclusively syntactic character such as that defined by Shannon, research advances (...) in recent decades have led not only to the definition of a second-order cybernetics but also to an exploration of the boundaries of semantic information. As H. Atlan states, on a biological level "the function self-organizes together with its meaning". Hence the need to refer to a conceptual theory of complexity and to a theory of self-organization characterized in an intentional sense. There is also a need to introduce, at the genetic level, a distinction between coder and ruler as well as the opportunity to define a real software space for natural evolution. The recourse to non-standard model theory, the opening to a new general semantics, and the innovative definition of the relationship between coder and ruler can be considered, today, among the most powerful theoretical tools at our disposal in order to correctly define the contours of that new conceptual revolution increasingly referred to as metabiology. This book focuses on identifying and investigating the role played by these particular theoretical tools in the development of this new scientific paradigm. Nature "speaks" by means of mathematical forms: we can observe these forms, but they are, at the same time, inside us as they populate our organs of cognition. In this context, the volume highlights how metabiology appears primarily to refer to the growth itself of our instruments of participatory knowledge of the world. (shrink)

This is a series of short summaries and brief overviews of many main ideas within general semantics, all couched in the style of personal letters. It is designed to give people an intimate view into many insights offered with general semantics, and just as equally, it represents how principles of general semantics can be applied within everyday life.

This paper presents Lewis's intensional semantics, on the basis of which he aims to answer two questions: “What sort of thing is a meaning?” and “What is the form of semantic rules whereby meanings of compounds are built from the meanings of their constituent parts?” To this end, Lewis develops a categorically based transformational grammar. The paper provides formal treatments of such topics as intensions (for both basic and derived categories), nondeclarative sentences, quantification, and noun‐phrases.

As H. Atlan and A. Carsetti remark in a natural self organizing system (a biological one, characterized by the existence of cognitive activities) the goal has not been set from the outside. What is self-organizing is the function itself with its meaning. The origin of meaning in the organization of the system is an emergent property. In this sense the origin of meaning is closely connected to precise linguistic and logical operations and to well defined procedures of observation and self-observation. (...) These operations and procedures induce, normally, continuous processes of inner reorganization at the level of the system. The behaviour of the net, in other words, possesses a meaning not only to the extent that it will result autonomous and to the extent that inside it we can inspect a continuous revelation of hidden properties, but also to the extent that it will result capable of observation and self-observation as well as intentionally linked to a continuous production of possible new interpretation acts and reorganization schemes. The state space relative to these observational, self-observational and intentional functional activities cannot be confined, in this sense, on logical grounds, only within the boundaries of a nested articulation of propositional Boolean frames. On the contrary, we will be obliged, in order to give an explanation, within a general theory of cellular nets, for such complex phenomena, to resort to particular informational tools that reveal themselves as essentially linked to the articulation of predicative and higher-order level languages, to the outlining of a multidimensional information theory and to the definition of an adequate intensional and second-order semantics. (shrink)

Contributing Authors Include Oliver L. Reiser, Alvin Priestly Bradford, Irving J. Lee, And Others. Non-Aristotelian Methodology Applied For Sanity In Our Time.

This paper introduces a generalized version of inquisitive semantics, denoted as GIS, and concentrates especially on the role of disjunction in this general framework. Two alternative semantic conditions for disjunction are compared: the first one corresponds to the so-called tensor operator of dependence logic, and the second one is the standard condition for inquisitive disjunction. It is shown that GIS is intimately related to intuitionistic logic and its Kripke semantics. Using this framework, it is shown that the (...) main results concerning inquisitive semantics, especially the axiomatization of inquisitive logic, can be viewed as particular cases of more general phenomena. In this connection, a class of non-standard superintuitionistic logics is introduced and studied. These logics share many interesting features with inquisitive logic, which is the strongest logic of this class. (shrink)

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.