On Łukasiewicz's Four-Valued Modal Logic

ukasiewicz's four-valued modal logic is surveyed and analyzed, together with ukasiewicz's motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz's own texts, and related literature.     

The completeness of the factor semantics for Łukasiewicz's infinite-valued logics

In [12] it was shown that the factor semantics based on the notion ofT-F-sequences is a correct model of the ukasiewicz's infinite-valued logics. But we could not consider some important aspects of the structure of this model because of the short size of paper. In this paper we give a more complete study of this problem: A new proof of the completeness of the factor semantic for ukasiewicz's logic using Wajsberg algebras [3] (and not MV-algebras in [1]) and Symmetrical Heyting monoids [7] is proposed. Some consequences of such an approach are investigated.     

Forcing in Łukasiewicz Predicate Logic

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀. Presented by Jacek Malinowski     

Proper n-valued Łukasiewicz algebras as S-algebras of Łukasiewicz n-valued prepositional calculi

Proper n-valued ukasiewicz algebras are obtained by adding some binary operators, fulfilling some simple equations, to the fundamental operations of n-valued ukasiewicz algebras. They are the s-algebras corresponding to an axiomatization of ukasiewicz n-valued propositional calculus that is an extention of the intuitionistic calculus.Dedicated to the memory of Gregorius C. Moisil     

The portrayal of women in prime time, 1953–1977

A content analysis of 1314 television programs and 2444 starring characters appearing on prime-time television from 1953–1977 revealed that the number of females in starring roles has remained relatively constant over the last 25 years and that most women are still found in situation comedies. While the number of women shown as housewives or housekeepers has declined from the 1950s to the present, the makeup of the television labor force has consistently shown no relationship to the real-life employment patterns of women. The data seem to support the findings announced in a recent study by the United States Commission on Civil Rights, which concluded that women were underrepresented on television and were frequently seen in stereotyped roles.     

Averaging the truth-value in Łukasiewicz logic

Chang's MV algebras are the algebras of the infinite-valued sentential calculus of ukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of average degree of truth of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC*-algebras stand to commutative AFC*-algebras, states are naturally related to noncommutativeC*-algebraic measures.     

A Generalization of the Łukasiewicz Algebras

We introduce the variety _n ^m , m 1 and n 2, of m-generalized ukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety _n ^m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety _n ^m contains the variety of ukasiewicz algebras of order n.     

A non-commutative generalization of Łukasiewicz rings

The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola [1] to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.     

Construction of monadic three-valued Łukasiewicz algebras

The notion of monadic three-valued ukasiewicz algebras was introduced by L. Monteiro ([12], [14]) as a generalization of monadic Boolean algebras. A. Monteiro ([9], [10]) and later L. Monteiro and L. Gonzalez Coppola [17] obtained a method for the construction of a three-valued ukasiewicz algebra from a monadic Boolea algebra. In this note we give the construction of a monadic three-valued ukasiewicz algebra from a Boolean algebra B where we have defined two quantification operations and ^* such that ^*x=^*x (where ^*x=-^*-x). In this case we shall say that and ^* commutes. If B is finite and is an existential quantifier over B, we shall show how to obtain all the existential quantifiers ^* which commute with .Taking into account R. Mayet [3] we also construct a monadic three-valued ukasiewicz algebra from a monadic Boolean algebra B and a monadic ideal I of B. The most essential results of the present paper will be submitted to the XXXIX Annual Meeting of the Unión Matemática Argentina (October 1989, Rosario, Argentina).     

On Łukasiewicz-Moisil algebras of fuzzy sets

The set (X, J) of fuzzy subsetsf:XJ of a setX can be equipped with a structure of -valued ukasiewicz-Moisil algebra, where is the order type of the totally ordered setJ. Conversely, every ukasiewicz-Moisil algebra — and in particular every Post algebra — is isomorphic to a subalgebra of an algebra of the form (X, J), whereJ has an order type . The first result of this paper is a characterization of those -valued ukasiewicz-Moisil algebras which are isomorphic to an algebra of the form (X, J) (Theorem 1). Then we prove that (X, J) is a Post algebra if and only if the setJ is dually well-ordered (Theorem 2) and we give a characterization of those -valued Post algebras with are isomorphic to an algebra of the form (X, J) (Theorem 3 and Proposition 2).     

Recreating Raven’s: Software for systematically generating large numbers of Raven-like matrix problems with normed properties

Raven’s Progressive Matrices is a widely used test for assessing intelligence and reasoning ability (Raven, Court, & Raven, 1998). Since the test is nonverbal, it can be applied to many different populations and has been used all over the world (Court & Raven, 1995). However, relatively few matrices are in the sets developed by Raven, which limits their use in experiments requiring large numbers of stimuli. For the present study, we analyzed the types of relations that appear in Raven’s original Standard Progressive Matrices (SPMs) and created a software tool that can combine the same types of relations according to parameters chosen by the experimenter, to produce very large numbers of matrix problems with specific properties. We then conducted a norming study in which the matrices we generated were compared with the actual SPMs. This study showed that the generated matrices both covered and expanded on the range of problem difficulties provided by the SPMs.