12,103 research outputs found
Advances in Proof-Theoretic Semantics
Logic; Mathematical Logic and Foundations; Mathematical Logic and Formal Language
Revisiting Dummett's Proof-Theoretic Justification Procedures
Dummett’s justification procedures are revisited. They are used as background for the discussion of some conceptual and technical issues in proof-theoretic semantics, especially the role played by assumptions in proof-theoretic definitions of validity
Indexed linear logic and higher-order model checking
In recent work, Kobayashi observed that the acceptance by an alternating tree
automaton A of an infinite tree T generated by a higher-order recursion scheme
G may be formulated as the typability of the recursion scheme G in an
appropriate intersection type system associated to the automaton A. The purpose
of this article is to establish a clean connection between this line of work
and Bucciarelli and Ehrhard's indexed linear logic. This is achieved in two
steps. First, we recast Kobayashi's result in an equivalent infinitary
intersection type system where intersection is not idempotent anymore. Then, we
show that the resulting type system is a fragment of an infinitary version of
Bucciarelli and Ehrhard's indexed linear logic. While this work is very
preliminary and does not integrate key ingredients of higher-order
model-checking like priorities, it reveals an interesting and promising
connection between higher-order model-checking and linear logic.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Programming in logic without logic programming
In previous work, we proposed a logic-based framework in which computation is
the execution of actions in an attempt to make reactive rules of the form if
antecedent then consequent true in a canonical model of a logic program
determined by an initial state, sequence of events, and the resulting sequence
of subsequent states. In this model-theoretic semantics, reactive rules are the
driving force, and logic programs play only a supporting role.
In the canonical model, states, actions and other events are represented with
timestamps. But in the operational semantics, for the sake of efficiency,
timestamps are omitted and only the current state is maintained. State
transitions are performed reactively by executing actions to make the
consequents of rules true whenever the antecedents become true. This
operational semantics is sound, but incomplete. It cannot make reactive rules
true by preventing their antecedents from becoming true, or by proactively
making their consequents true before their antecedents become true.
In this paper, we characterize the notion of reactive model, and prove that
the operational semantics can generate all and only such models. In order to
focus on the main issues, we omit the logic programming component of the
framework.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
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