Neighborhood Semantics for Basic and Intuitionistic Logic

Moniri, Morteza; Maleki, Fatemeh Shirmohammadzadeh

doi:10.12775/llp.2015.015

Cited by 8 publications

(6 citation statements)

References 4 publications

(5 reference statements)

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“…Neighborhoods for pure intuitionistic logic (i.e. without modalities) have been introduced by Moniri and Maleki in [6]. If we speak about classical modal logic, then we should note that Pacuit presented an interesting survey of neighborhood semantics for such systems in [7].…”

Section: Neighborhood Semanticsmentioning

confidence: 99%

Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic

Witczak

2019

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We present three examples of multi-topological semantics for intuitionistic modal logic with one modal operator (which behaves in some sense like necessity). We show that it is possible to treat neighborhood models, introduced earlier, as multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multi-topological spaces into the neighborhood structures.arXiv:1903.06900v1 [math.LO]

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Section: Neighborhood Semanticsmentioning

confidence: 99%

Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic

Witczak

2019

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“…As for the neighborhood semantics for intuitionistic logic, it has been presented by Moniri and Maleki in [4]. They have also considered simple subintuitionistic case of BPL (Basic Propositional Logic).…”

Section: Neighborhood Semantics 21 Foundations Of Neighborhood Semanticsmentioning

confidence: 99%

“…The notions of bounded morphism and bisimulation are well-known and widely used by researchers working with relational (Kripke) or neighborhood models. In this chapter we show how those tools can be used in our environment (see also [4] for comparison). Note that in the fourth subsection our new connective becomes really necessary.…”

Section: Bisimulation and Congenial Notionsmentioning

confidence: 99%

Intuitionistic modal logic based on neighborhood semantics without superset axiom

Witczak

2017

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In this paper we investigate certain systems of propositional intuitionistic modal logic defined semantically in terms of neighborhood structures. We discuss various restrictions imposed on those frames but our constant approach is to discard superset axiom. Such assumption allows us to think about specific modalities ∆, ∇ and new functor depending on the notion of maximal neighborhood. We show how it is possible to treat our models as bi-relational ones.We prove soundness and completeness of proposed axiomatization by means of canonical model.Moreover, we show that finite model property holds. Then we describe properties of bounded morphism, behavioral equivalence, bisimulation and n-bisimulation. Finally, we discuss further researches (like some interesting classical cases and particular topological issues).

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“…In [9] we established sound and complete semantics based on the notion of neighborhoods. In fact, we modified typical neighborhood semantics for intuitionism (presented in [5]) by removing superset axiom. Thus, we could speak not only about minimal neighborhoods of worlds -but also about maximal ones.…”

Section: Introductionmentioning

confidence: 99%

Simple example of weak modal logic based on intuitionistic core

Witczak

2018

Preprint

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In this paper we present simple example of propositional logic which has one modal operator and is based on intuitionistic core. This system is very weak in modal sense -e.g. rules of regularity or monotonicity do not hold. It has complete semantics composed of possible worlds equipped with neighborhoods and pre-order relation. We discuss certain restrictions imposed on those structures. Also, we present characterization of axiom 4 known from logic S4 .

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Neighborhood Semantics for Basic and Intuitionistic Logic

Cited by 8 publications

References 4 publications

Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic

Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic

Intuitionistic modal logic based on neighborhood semantics without superset axiom

Simple example of weak modal logic based on intuitionistic core

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