
A Rice's Theorem for Abstract Semantics
Classical results in computability theory, notably Rice's theorem, focus...
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On Signings and the WellFounded Semantics
In this note, we use Kunen's notion of a signing to establish two theore...
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Axiomatizations and Computability of Weighted Monadic SecondOrder Logic
Weighted monadic secondorder logic is a weighted extension of monadic s...
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Leveraging Declarative Knowledge in Text and FirstOrder Logic for FineGrained Propaganda Detection
We study the detection of propagandistic text fragments in news articles...
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A proof theoretic basis for relational semantics
Logic has proved essential for formally modeling software based systems....
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Theorem Proving and Algebra
This book can be seen either as a text on theorem proving that uses tech...
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ERIC: Extracting Relations Inferred from Convolutions
Our main contribution is to show that the behaviour of kernels across mu...
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On the Semantics of Intensionality and Intensional Recursion
Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality. This is a familiar setting for computer scientists, who often study different programs or processes that are interchangeable, i.e. extensionally equal, even though they are not implemented in the same way, so intensionally distinct. Concomitant with intensionality is the phenomenon of intensional recursion, which refers to the ability of a program to have access to its own code. In computability theory, intensional recursion is enabled by Kleene's Second Recursion Theorem. This thesis is concerned with the crafting of a logical toolkit through which these phenomena can be studied. Our main contribution is a framework in which mathematical and computational constructions can be considered either extensionally, i.e. as abstract values, or intensionally, i.e. as finegrained descriptions of their construction. Once this is achieved, it may be used to analyse intensional recursion.
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