On a coalgebraic view on Logic

Hofmann, Dirk; Martins, Manuel A.

doi:10.1093/logcom/exs063

Journal of Logic and Computation

2012

DOI: 10.1093/logcom/exs063

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On a coalgebraic view on Logic

Dirk Hofmann¹,

Manuel A. Martins²

Abstract: In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category.

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2014

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The role of logical interpretations in program development

Martins¹,

Madeira²,

Barbosa³

2014

Logical Methods in Computer Science

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Abstract. Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant transformations in the context of software design, reuse, and adaptation. This paper proposes a new approach to refinement in which signature morphisms are replaced by logical interpretations as a means to witness refinements. The approach is first presented in the context of equational logic, and later generalised to deductive systems of arbitrary dimension. This allows, for example, refining sentential into equational specifications and the latter into modal ones.

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The role of logical interpretations in program development

Martins¹,

Madeira²,

Barbosa³

2014

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

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On a coalgebraic view on Logic

Abstract: In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category.

Cited by 1 publication

References 10 publications

The role of logical interpretations in program development

The role of logical interpretations in program development

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