2,023 research outputs found
Genuine Process Logic
The Genuine Process Logic described here (abbreviation: GPL) places the object-bound process itself at the center of formalism. It should be suitable for everyday use, i.e. it is not primarily intended for the formalization of computer programs, but instead, as a counter-conception to the classical state logics. The new and central operator of the GPL is an action symbol replacing the classical state symbols, e.g. of equivalence or identity. The complete renunciation of object-language state expressions also results in a completely new metalinguistic framework, both regarding the axioms and the expressive possibilities of this system. A mixture with state logical terms is readily possible
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
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
Refinement Modal Logic
In this paper we present {\em refinement modal logic}. A refinement is like a
bisimulation, except that from the three relational requirements only `atoms'
and `back' need to be satisfied. Our logic contains a new operator 'all' in
addition to the standard modalities 'box' for each agent. The operator 'all'
acts as a quantifier over the set of all refinements of a given model. As a
variation on a bisimulation quantifier, this refinement operator or refinement
quantifier 'all' can be seen as quantifying over a variable not occurring in
the formula bound by it. The logic combines the simplicity of multi-agent modal
logic with some powers of monadic second-order quantification. We present a
sound and complete axiomatization of multi-agent refinement modal logic. We
also present an extension of the logic to the modal mu-calculus, and an
axiomatization for the single-agent version of this logic. Examples and
applications are also discussed: to software verification and design (the set
of agents can also be seen as a set of actions), and to dynamic epistemic
logic. We further give detailed results on the complexity of satisfiability,
and on succinctness
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