229 research outputs found
A system of relational syllogistic incorporating full Boolean reasoning
We present a system of relational syllogistic, based on classical
propositional logic, having primitives of the following form:
Some A are R-related to some B;
Some A are R-related to all B;
All A are R-related to some B;
All A are R-related to all B.
Such primitives formalize sentences from natural language like `All students
read some textbooks'. Here A and 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.Comment: Available at
http://link.springer.com/article/10.1007/s10849-012-9165-
Logics for the Relational Syllogistic
The Aristotelian syllogistic cannot account for the validity of many
inferences involving relational facts. In this paper, we investigate the
prospects for providing a relational syllogistic. We identify several fragments
based on (a) whether negation is permitted on all nouns, including those in the
subject of a sentence; and (b) whether the subject noun phrase may contain a
relative clause. The logics we present are extensions of the classical
syllogistic, and we pay special attention to the question of whether reductio
ad absurdum is needed. Thus our main goal is to derive results on the existence
(or non-existence) of syllogistic proof systems for relational fragments. We
also determine the computational complexity of all our fragments
Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972
Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others.
Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic
An examination of Aristotelian modality
From introduction: A popular misconception regarding Aristotle's views on modality is that Aristotle adhered to the doctrine of no unrealized possibilities. According to this doctrine, all possibilities are realized in time; in other words, if it is possible that something could happen, then at some time it is the case that that happens. For example, if it is possible for Socrates to escape from prison, then there will be a time at which Socrates will actually escape from prison. On this view, the possible and the actual co-incide; whereas there is abundant evidence that Aristotle was careful to maintain a distinction between the possible and the actual
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