# Arithmetizations of Syllogistic à la Leibniz

@article{Sotirov1999ArithmetizationsOS, title={Arithmetizations of Syllogistic {\`a} la Leibniz}, author={V. Sotirov}, journal={J. Appl. Non Class. Logics}, year={1999}, volume={9}, pages={387-405} }

Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea. In the interpretation, called Scholastic, terms are replaced by integer...

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#### References

SHOWING 1-9 OF 9 REFERENCES

Aristotelian syllogisms and generalized quantifiers

- Mathematics, Computer Science
- Stud Logica
- 1989

The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern… Expand

On the Interpretation of Aristotelian Syllogistic

- Mathematics, Computer Science
- J. Symb. Log.
- 1956

(theorem 6, ? 4) we show that in Wedberg's system [14] with primitives 'Aab', 'a" (not a), it is possible to find a mapping a -T(a) as above such that 'Aab' is equivalent to '92(a) is contained in… Expand

Generalized quantifiers and modal logic

- Mathematics, Computer Science
- J. Log. Lang. Inf.
- 1993

Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. Expand

Computability and logic

- Mathematics, Computer Science
- 1974

This book discusses Computability Theory, Modal logic and provability, and its applications to first-order logic, which aims to clarify and clarify the role of language in the development of computability. Expand

Set Containment Inference and Syllogisms

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 1988

Necessary and sufficient conditions for consistency, as well as sound and complete sets of inference rules, are presented for binary containment inference, which is solved by rules essentially equivalent to Aristotle's syllogisms. Expand

Information Systems, Similarity Relations and Modal Logics

- Computer Science
- 1998

The completeness theorems for the introduced modal logics with respect to their standard semantics are introduced and their “query meaning” is discussed. Expand

Cardinalities of Models for Pure Calculi of Names

- Mathematics, Computer Science
- Reports Math. Log.
- 1994