Omyla, Mieczyslaw. 1976. "Translatability in Non-Fregean Theories." Studia Logica no. 35:127-138.
———. 1978. "Boolean Theories with Quantifiers." Bulletin of the Section of Logic no. 7:76-83.
———. 1982. "The Logic of Situations." In Language and Ontology. Proceedings of the 6th International Wittgenstein Symposium. 23rd to 30th August 1981 Kirchber Am Wechsel
(Austria), edited by Leinfellner, Werner, Kraemer, Eric and Schamk, Jeffrey, 195-198. Wien: Hölder-Pichler-Tempsky.
"Professor Roman Suszko introduced a broad class of languages into the literature of logic. In honour of Wittgenstein Suszko named these languages W-languages. Syntax, semantics and
consequence operations in these languages are based on the famous ontological principle: whatever exists is either a situation, or an object, or a function. The distinguishing property of W-languages
is that they contain sentential and nominal variables, identity connectives and identity predicates. The intended interpretation of W-languages is such that sentential variables range over the
universum of situations, nominal variables range over the universum of objects. All other symbols in these languages except sentential and nominal variables are interpreted as symbols of some
functions both defined over the universum of situations and the universum of objects. Identity connectives correspond to identity relations between situations, and identity predicates correspond to
identity relations between objects. It is obvious that the ordinary predicate calculus with identity is a part W-language excluding sentential variables, but the most often used sentential languages
are the part of W-languages without nominal variables and identity predicates. In this paper, I will discuss only W-languages containing sentential variables, connectives and possibly quantifiers
binding sentential variables." p. 195
———. 1982. "Basic Intuitions of Non-Fregean Logic." Bulletin of the Section of Logic no. 11:40-47.
———. 1989. "Non-Fregean Logic and Ontology of Situations." Ruch Filozoficzny no. 47:27-30.
———. 1990. "The Principles of Non-Fregean Semantics for Sentences." Journal of Symbolic Logic no. 55:422-423.
———. 1994. "Non-Fregean Semantics for Sentences." In Philosophical Logic in Poland, edited by Wolenski, Jan, 153-165. Dordrecht: Kluwer Academic Publishers.
"In this paper I intend to present the general and formal principles of non-Fregean semantics for sentences and to derive the simplest consequences of these principles. The semantic
principles constitue foundation of non-Fregean sentential calculus and its formal semantics and the philosophical interpretations of it. Non-Fregean sentential calculus is the basic part of
non-Fregean logic. Non-Fregean logic is a generalization of classical logic. It was conceived by Roman Suszko under the influence of Wittgensteinian's Tractatus Logico-Philosophicus. The
term "non-Fregean" indicates that the set of semantic correlate of sentences need not contain of just two elements, as it assumed by Frege in Über Sinn und Bedeuting (1892). Frege accepted
the following semantic principle:
(A.F.) all true sentences have the same common referent, and similarly all false sentences also have the one common referent.
J. Lukasiewicz interpreted the common referent of true sentences as "Being" and analogically the common referent of all false sentences as "Unbeing". Suszko called the principle
(A.F) the "semantical version of the Frege an axiom".
In Abolition of the Frgean Axiom (1975) Suszko wrote: "If one accepts the Fregean Axiom then one is compelled to be an absolute monist in the sense that there exists only
one and necessary fact".
According to Suszko (A. F.) has a counterpart in the language of classical logic which is a formula asserting that the universe of sentential variables is a two-element set. This
formula is not expressed that fact in the language of non-Fregean logic.
In SCI and modal systems (1972) Suszko presents the properties of his logic as follows: "... nonFregean logic is the realization of the Fregean program in pure logic,
logically bi-valent and extensional with two modifications: (1) keep formulas (sentences) and termes (names) as disjoint syntactic categories, having sense and denotations,as well, and (2) drop the
desperate assumption that all true or false senetences have the same denotation (not sense that is proposition)"." pp. 153-154.
———. 1996. "A Formal Ontology of Situations." In Formal Ontology, edited by Poli, Roberto and Simons, Peter M., 173-187. Dordrecht: Kluwer Academic Publishers.
"The theoretical foundation for this paper is the system of a non-Fregean logic created by Roman Suszko under the influence of Wittgenstein's Tractatus
Logico-Philosophicus. In fact, we use just a fragment of it called here a non-Fregean sentential logic.
Our basic term is that of a 'situation'. We do not answer the question what situations are. We simply assume that sentences present situations, and we provide a criterion
determining when two sentences of some fixed language present the same situation.
The lay-out of this paper is the following. First we set out certain philosophical consequences of the assumption adopted in classical logic that the only connectives of the
language in question are the truth-functional ones. Then we sketch out briefly the axiomatics of non-Fregean sentential logic, and of a formal semantics of the algebraic type for it.
Next, for an arbitrary model for a non-Fregean sentential logic, we pick out from the formulae true in that model a theory to be called the 'ontology of situations determined by the
model in question' - in contradistinction to all sentences holding contingently in that model, i.e. not determined by its algebra. In the ontology of situations determined by a model we point out
those propositions which pertain to possible worlds." p. 173
Philosophical Interpretations of non-Fregean Sentential Logic
According to the principles of non-Fregean semantics as presented in Omyla 1975, all sentences of an interpreted language have their references. However, not in every such language
are we in a position to put forward universal and existential theorems with regard to the structure of the universe of those references. To be in such position the language in question must contain
as its sublanguage the language of non-Fregean sentential logic, or at least a significant part of it. As we are not interested here in the universe of any particular language, but only in that of a
quite arbitrary one, let us consider now some philosophical aspects of arbitrary models of that kind. Let M = (U, F) be such a model. The elements of the universe of U do not generally answer to the
intuitions we have about the reference of sentences, and about situations in particular. However, the algebraic structure imposed on U by the theory TR(M) is the same as that of a possible universe
of situations, with regard to the operations corresponding to logical constants. Moreover, the set F has the formal properties of a possible (or 'admissible') set of situations obtaining in that
universe. This is so because sentential variables are at the same time sentential formulae, and because the logical constants get in the model M their intended interpretation. Thus for any model M =
(U, F) its algebra U is a formal representation of some universe of situations, and the set F is a formal representation of some admissible set of facts obtaining in some universe of situations. Not
all the generalized SCI-algebras represent some algebra of situations; for not all of them contain a set F representing the facts, i.e. such that the couple (U, F) is a model. This depends on how the
operations in the algebra U are defined. For the sake of simplicity the algebra of any model M = (U, F) for the language of a non-Fregean sentential logic will be called the algebra of
situations occurring in the model M, and the designated set F will be called the set of facts obtaining in M. Such a terminology is appropriate here for we are interested only in the
formal properties of those universe of situations which in view of our semantic principles find expression in the logical syntax of the language in question, and in consequence operation holding in
it. By the completeness theorem for non-Fregean logic it follows that for any consistent theory T in L there is a model M such that T e TR(M). Hence any theory in the language of non-Fregean
sentential logic will be called a theory of situations.
The term 'ontology of situations' we take over from the title of Wolniewicz 1985 [ Ontologia sytuacji: Ontology of situations in Polish], but we understand it a bit
differently. By an ontology of situations we mean a theory describing the necessary facts of universe of situations fixed beforehand. I.e. an ontology of situations is a set of formulae
holding in some fixed universe of situations, independently of which situations there are facts. To be more accurate, by an ontology of situations we mean a set of formulae with the following three
( 1) An ontology of situations is a theory having in its vocabulary just one kind of variable - e. the sentential one. Under the intended interpretation they range over a universe
of situations. (Like in modem set theory there are variables of just one kind, i.e. those ranging over sets.)
(2) An ontology of situations is formulated in a language containing logical symbols only, i. e. logical constants and variables. To justify that postulate let us note that such a
basic theory should not presuppose any other terminology except the logical one. At most it might adopt some specific ontological terms as primitive, characterizing them axiomatically. However, we
shall deal here only with such ontologies of situations which are expressed exclusively in logical terms." pp. 180-181.
———. 2003. "Possible Worlds in the Language of Non-Fregean Logic." Studies in Logic, Grammar and Rhetoric no. 6:7-15.
"The term "possible world" is used usually in the metalanguage of modal logic, and it is applied to the interpretation of modal connectives. Surprisingly, as it has been shown in
Suszko Ontology in the Tractatus L. Wittgenstein (1968) certain versions of that notion can be defined in the language of non-Fregean logic exclusively, by means of sentential variables and
logical constants. This is so, because some of the non-Fregean theories contain theories of modality, as shown in Suszko Identity Connective and Modality (1971).
Intuitively, possible worlds are maximal (with respect to an order of situations) and consistent situations, while the real world may be understand as a situation, which is a
possible world and the fact.
Non-Fregean theories are theories based on the non-Fregean logic. Non-Fregean logic is the logical calculus created by Polish logician Roman Suszko in the sixties. The idea of that
calculus was conceived under the influence of Wittgenstein's Tractatus. According to Wittgenstein, declarative sentences of any language describe situations."