Interpretation Of Logical Connectives Research Articles

The interpretation of logical connectives in Turkish.

This study investigated how Turkish-speaking children and adults interpret negative sentences with disjunction (English or) and ones with conjunction (English and). The goal was to see whether Turkish-speaking children and adults assigned the same interpretation to both kinds of sentences and, if not, to determine the source of the differences. Turkish-speaking children and adults were found to assign different interpretations to negative sentences with disjunction just in case the nouns in the disjunction phrase were marked with accusative case. For children, negation took scope over disjunction regardless of case marking, whereas, for adults, disjunction took scope over negation if the disjunctive phrases were case marked. Both groups assigned the same interpretation to negative sentences with conjunction; both case-marked and non-case-marked conjunction phrases took scope over negation. The findings are taken as evidence for a 'subset' principle of language learnability that dictates children's initial scope assignments.

Complexity of Sets Obtained as Values of Propositional Formulas

Interpretation of logical connectives as operations on sets of binary strings is considered; the complexity of a set is defined as the minimum of Kolmogorov complexities of its elements. It is readily seen that the complexity of a set obtained by the application of logical operations does not exceed the complexity of the conjunction of their arguments (up to an additive constant). In this paper, it is shown that the complexity of a set obtained by a formula Φ is small (bounded by a constant) if Φ is deducible in the logic of weak excluded middle, and attains the specified upper bound otherwise.

Local possibilistic logic

ABSTRACT Possibilistic states of information are fuzzy sets of possible worlds. They constitute a complete lattice, which can be endowed with a monoidal operation (a t-norm) to produce a quantal. An algebraic semantics is presented which links possibilistic formulae with information states, and gives a natural interpretation of logical connectives as operations on fuzzy sets. Due to the quantal structure of information states, we obtain a system which shares several features with (exponential-free) intuitionistic linear logic. Soundness and completeness are proved, parametrically on the choice of the t-norm operation.

Conjunctive Interpretations of Logical Connectives: Replication of Results Using a New Type of Task

In an earlier study Damarin (1977) reported on the performance of subjects who were asked to judge the truth falsity of compound statements concerning membership of elements in pictured sets. More than 90% of these subjects-preservice elementary teachers-were found to treat both conditional and biconditional statements as conjunctions. Roughly half the population also treated the disjunction as a conjunction, whereas less than a third handled it correctly as inclusive or; only one subject treated the or exclusively. These findings contrast sharply with those of other researchers, who have found that similar subjects' performance on inference tasks can often be attributed to exclusive interpretations of or (Juraschek, Note 1) and treatment of conditional statements as if they were biconditional (O'Brien, Shapiro, & Reali, 1971). The tasks used by these researchers involve pairs of statements about familiar objects (e.g., dogs, balls, brothers) and ask subjects to indicate whether certain inferences can be drawn. The purpose of the present study was to examine subjects' interpretations of logical connectives when they appear in single statements concerning mathematical relations.

Brief Reports: Conjunctive Interpretations of Logical Connectives: Replication of Results Using a New Type of Task

In an earlier study Damarin (1977) reported on the performance of subjects who were asked to judge the truth or falsity of compound statements concerning membership of elements in pictured sets. More than 90% of these subjects—preservice elementary teachers—were found to treat both conditional and biconditional statements as conjunctions. Roughly half the population also treated the disjunction as a conjunction, whereas less than a third handled it correctly as “inclusive or”; only one subject treated the “or” exclusively.