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Course Notes in Typed Lambda Calculus
, 1998
"... this paper is clearly stated, after recalling how the logical connectives can be explained in term of the Sheffer connective: "We are led to the idea, which at first glance certainly appears extremely bold of attempting to eliminate by suitable reduction the remaining fundamental notions, those ..."
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this paper is clearly stated, after recalling how the logical connectives can be explained in term of the Sheffer connective: "We are led to the idea, which at first glance certainly appears extremely bold of attempting to eliminate by suitable reduction the remaining fundamental notions, those of proposition, propositional function, and variable, from those contexts in which we are dealing with completely arbitrary, logical general propositions . . . To examine this possibility more closely and to pursue it would be valuable not only from the methodological point of view that enjoins us to strive for the greatest possible conceptual uniformity but also from a certain philosophic, or if you wish, aesthetic point of view."
Hybrid Type Theory: A Quartet in Four Movements
"... This paper sings a song — a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin ..."
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This paper sings a song — a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities (these can be found in Areces, Blackburn, Huertas, and Manzano [3]) rather it focusses on the underlying instruments, and the way they work together. We hope the reader will be tempted to sing along. This paper is about a logic... and about beauty. It tells the story of an idea born by bringing together the work of four great names in the history of logic. The ideas of Hans Reichenbach on the importance of temporal reference and those of Arthur Prior on the importance of the internal perspective provided by modal and tense logic were first combined in [5]. In that paper, a simple hybrid logic (namely, propositional nominal tense logic) allowed the insights of Reichenbach and Prior to be integrated. A decade later,
Fine’s Theorem on FirstOrder Complete Modal Logics
, 2011
"... Fine’s Canonicity Theorem states that if a modal logic is determined by a firstorder definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result, and the history of its influence on further research. It then develops a n ..."
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Fine’s Canonicity Theorem states that if a modal logic is determined by a firstorder definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result, and the history of its influence on further research. It then develops a new characterisation of when a logic is canonically valid, providing a precise point of distinction with the property of firstorder completeness. 1 The Canonicity Theorem and Its Impact In his PhD research, completed in 1969, and over the next halfdozen years, Kit Fine made a series of fundamental contributions to the semantic analysis and metatheory of propositional modal logic, proving general theorems about notable classes of logics and providing examples of failure of some significant properties. This work included the following (in order of publication): • A study [6] of logics that have propositional quantifiers and are defined