Results 171 to 180 of about 214 (213)

Logicism, Neo-Logicism, and the Logics of Abstraction

2023
Abstraction principles play a pivotal role in the foundations of mathematics. In the foundational programs in which they have been traditionally adopted, i.e. Frege’s logicism and Scottish neo-logicism, abstraction principles, conceived as definitions, augment a system of full higher-order logic.
Boccuni, Francesca, Sereni, Andrea
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Embedding Logics into Product Logic

Studia Logica, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matthias Baaz, Petr Hájek 0001, David Svejda, Jan Krajícek   +3 more
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A Verification Logic for Rewriting Logic

Journal of Logic and Computation, 2005
Summary: This paper proposes the development of a logic for verifying properties of programs in rewriting logic. Rewriting logic is primarily a logic of change, in which deduction corresponds directly to computation, and not a logic to talk about change in a more indirect and global manner, such as the different modal and temporal logics that can be ...
Narciso Martí-Oliet, Isabel Pita, José Luiz Fiadeiro, José Meseguer 0001, T. S. E. Maibaum   +4 more
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Modal Logic As Dialogical Logic

Synthese, 2001
The title reflects my conviction that, viewed semantically, modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy.
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Logic Programming and Default Logic

International Journal on Artificial Intelligence Tools, 1994
We present several ideas of increasing complexity how to translate default theories to normal logic programs that make direct use of the deductive capacity of logic programming. We show the limitations of simple, ad hoc approaches, and arrive at a more general construction; its main property is that the answer substitutions computed by the logic ...
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Intuitionistic Logic As Epistemic Logic

Synthese, 2001
Is intuitionism a variant of constructivism? If intuitionism is not constructivism, what is it? What do the intuitions of the genuine intuitionists add up to? Are their intentions reflected faithfully in Heyting's intuitionistic logic? What is the epistemic logic like, in which the distinction can be made and in which the correctly understood claims of
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Abstract Logics, Logic Maps, and Logic Homomorphisms

Logica Universalis, 2007
What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations of a general theory of abstract logics which is based on the abstract concept of a theory.
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Logic is not Logic

2021
In this paper we discuss the difference between logic as reasoning and logic as a theory about reasoning. In the light of this distinction we examine central questions about history, philosophy and the very nature of logic. We study in which sense we can consider Aristotle as the first logician, Descartes‘s rejection of syllogistic as logical, Boole ...
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The logic of optics and the optics of logic

Information Sciences, 2004
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H. John Caulfield, Jonathan Westphal
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Adaptive Logic as a Modal Logic

Studia Logica, 2012
Modal logic has received a tremendous push in the recent decades. However, its connection to non-classical logics (broadly conceived) still remains under-studied. Allo's paper studies a long-due gap in the field of adaptive logics, which is a subject mainly developed by Batens' research group.
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