Frege's Theorem
- G. Antonelli
- Philosophy
- 1 June 2012
Frege’s original logicist programme envisaged the derivation of arithmetical truths from a theory that could be characterized, in some sense, as ‘logic plus definitions’, thereby establishing the…
Forward Induction *
- G. Antonelli, C. Bicchieri
- Economics
- 2005
In this paper we isolate a particular refinement of the notion of Nash equilibrium that is characterized by two properties: (i) it provides a unified framework for both backwards and forward…
The Complexity of Revision
- G. Antonelli
- MathematicsNotre Dame J. Formal Log.
- 19 January 1994
The upper bound on the complexity of the Gupta-Belnap systems is established through a reduction to countable revision sequences that is inspired by, and makes use of a construction of McGee.
Notions of Invariance for Abstraction Principles
- G. Antonelli
- Philosophy
- 1 October 2010
The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character ‐ permutation…
Representability in second-order propositional poly-modal logic
- G. Antonelli, R. Thomason
- PhilosophyJournal of Symbolic Logic (JSL)
- 1 September 2002
This paper establishes the definability of the transitive closure of finitely many modal operators, and shows that the second-order propositional logic of two S5 modalitities is also equivalent to full second- order logic.
ON THE GENERAL INTERPRETATION OF FIRST-ORDER QUANTIFIERS
- G. Antonelli
- PhilosophyThe Review of Symbolic Logic
- 25 October 2013
This paper explores some of the consequences of such “general” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.
University of California at Berkeley Berkeley, CA, USA March 24–27, 2011
- G. Antonelli, L. Bienvenu, S. Thomas
- History
- 2012
Numerical Abstraction via the Frege Quantifier
- G. Antonelli
- PhilosophyNotre Dame J. Formal Log.
- 20 April 2010
A formalization of rst-order arith- metic characterizing the natural numbers as abstracta of the equinumerosity relation is presented, turning on the interac- tion of a non-standard (but still rSt-order) cardinality quantier with an abstraction operator assigning objects to predicates.
Proto-Semantics for Positive Free Logic
- G. Antonelli
- PhilosophyJournal of Philosophical Logic
- 1 June 2000
This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of…
Game-theoretic axioms for local rationality and bounded knowledge
- C. Bicchieri, G. Antonelli
- Economics, Computer ScienceJournal of Logic, Language and Information
- 1 June 1995
It is shown that whenever the theory of the game is group-knowledge among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes and therefore means that players have distributed knowledge of it.
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