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Term Context

100%

Bancerek G.

Formalized Mathematics

2014

tom 22

nr 2

125-155

Two construction functors: simple term with a variable and compound term with an operation and argument terms and schemes of term induction are introduced. The degree of construction as a number of used operation symbols is defined. Next, the term context is investigated. An x-context is a term which includes a variable x once only. The compound term is x-context iff the argument terms include an x-context once only. The context induction is shown and used many times. As a key concept, the context substitution is introduced. Finally, the translations and endomorphisms are expressed by context substitution.

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A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB

63%

Inoue T.

Bulletin of the Section of Logic

2021

tom 50

nr 4

455-463

In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\), (M2) \(I^M(\neg \phi) = \neg I^M(\phi)\), (M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\), where \(p_a\) and \(p_b\) are propositional variables corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures.

Ograniczanie wyników

1 Bulletin of the Section of Logic

1 Formalized Mathematics

1 Bancerek G.

1 Inoue T.

1 2021

1 2015

Wyniki wyszukiwania

Term Context

A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB