A System of Relational Syllogistic Incorporating Full Boolean Reasoning


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Abstract
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘ All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem
Keywords Relational syllogistics  Completeness  Complexity
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DOI 10.1007/s10849-012-9165-1
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References found in this work BETA

Logics for the Relational Syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
Fragments of Language.Ian Pratt-Hartmann - 2004 - Journal of Logic, Language and Information 13 (2):207-223.
Complexity of the Two-Variable Fragment with Counting Quantifiers.Ian Pratt-Hartmann - 2005 - Journal of Logic, Language and Information 14 (3):369-395.

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Citations of this work BETA

Equivalential Structures for Binary and Ternary Syllogistics.Selçuk Topal - 2018 - Journal of Logic, Language and Information 27 (1):79-93.

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