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1

Plantinga’s Haecceitism and Simple Quantified Modal Logic

100%

Pavone L.

Logic and Logical Philosophy

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2018

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vol. 27

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issue 2

151-160

XX

In a series of papers Alvin Plantinga argued for a serious actualist modal semantics based on the notions of possible world, understood as maximal possible state of affairs, and of individual essence (haecceity). Plantinga’s actualism is known as haecceitism. In spite of the fact that haecceitism has been thought by Plantinga to require a Kripke-style semantics, the aim of this paper is to show that it is compatible with constant domains semantics and the simplest quantified modal logic. I will argue that not only does this approach have all the advantages of a greater simplicity in combining quantification and modalities, but also it better conforms to the actualist program.

2

Distributed Relation Logic

88%

Allwein G., Harrison W. L., Reynolds T.

Logic and Logical Philosophy

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2017

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vol. 26

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issue 1

19–61

EN

We extend the relational algebra of Chin and Tarski so that it is multisorted or, as we prefer, typed. Each type supports a local Boolean algebra outfitted with a converse operator. From Lyndon, we know that relation algebras cannot be represented as proper relation algebras where a proper relation algebra has binary relations as elements and the algebra is singly-typed. Here, the intensional conjunction, which was to represent relational composition in Chin and Tarski, spans three different local algebras, thus the term distributed in the title. Since we do not rely on proper relation algebras, we are free to re-express the algebras as typed. In doing so, we allow many different intensional conjunction operators. We construct a typed logic over these algebras, also known as heterogeneous algebras of Birkhoff and Lipson. The logic can be seen as a form of relevance logic with a classical negation connective where the Routley-Meyer star operator is reified as a converse connective in the logic. Relevance logic itself is not typed but our work shows how it can be made so. Some of the properties of classical relevance logic are weakened from Routley-Meyer’s version which is too strong for a logic over relation algebras.

3

Neighborhood Semantics for Basic and Intuitionistic Logic

75%

Moniri M., Maleki F. S.

Logic and Logical Philosophy

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2015

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vol. 24

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issue 3

339–355

EN

In this paper we present a neighborhood semantics for Intuitionistic Propositional Logic (IPL). We show that for each Kripke model of the logic there is a pointwise equivalent neighborhood model and vice versa. In this way, we establish soundness and completeness of IPL with respect to the neighborhood semantics. The relation between neighborhood and topological semantics are also investigated. Moreover, the notions of bisimulation and n-bisimulation between neighborhood models of IPL are defined naturally and some of their basic properties are proved. We also consider Basic Propositional Logic (BPL), a logic weaker than IPL introduced by Albert Visser, and introduce and study its neighborhood models in the same manner.

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3 Logic and Logical Philosophy

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1 Allwein G.

1 Harrison W. L.

1 Maleki F. S.

1 Moniri M.

1 Pavone L.

1 Reynolds T.

Plantinga’s Haecceitism and Simple Quantified Modal Logic

Distributed Relation Logic

Neighborhood Semantics for Basic and Intuitionistic Logic