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Frege's Theorem
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 theExpand
Notions of Invariance for Abstraction Principles
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 ‐ permutationExpand
The Complexity of Revision
  • G. Antonelli
  • Mathematics, Computer Science
  • Notre Dame J. Formal Log.
  • 19 January 1994
TLDR
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. Expand
Forward Induction *
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 forwardExpand
Representability in second-order propositional poly-modal logic
TLDR
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. Expand
Numerical Abstraction via the Frege Quantifier
  • G. Antonelli
  • Computer Science
  • Notre Dame J. Formal Log.
  • 20 April 2010
TLDR
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. Expand
ON THE GENERAL INTERPRETATION OF FIRST-ORDER QUANTIFIERS
  • G. Antonelli
  • Computer Science, Mathematics
  • The Review of Symbolic Logic
  • 25 October 2013
TLDR
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. Expand
Proto-Semantics for Positive Free Logic
  • G. Antonelli
  • Mathematics, Computer Science
  • J. Philos. Log.
  • 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 ofExpand
Game-theoretic axioms for local rationality and bounded knowledge
TLDR
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. Expand
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