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Synthese

pp 1–24 | Cite as

What is a logical theory? On theories containing assertions and denials

  • Carolina Blasio
  • Carlos Caleiro
  • João MarcosEmail author
S.I.: Varieties of Entailment

Abstract

The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper.

Keywords

Logical consequence Bilateralism The notion of theory Assertions and denials 

Notes

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.CampinasBrazil
  2. 2.SQIG–Instituto de TelecomunicaçõesLisbonPortugal
  3. 3.Dep. Matemática–Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  4. 4.LoLITA–DIMApUFRNNatalBrazil

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