373 research outputs found
Aximo: automated axiomatic reasoning for information update
Aximo is a software written in C++ that verifies epistemic properties of dynamic scenarios in multi-agent systems. The underlying logic of our tool is based on the algebraic axiomatics of Dynamic Epistemic Logic. We also present a new theoretical result: the worst case complexity of the verification problem of Aximo
Failure of interpolation in the intuitionistic logic of constant domains
This paper shows that the interpolation theorem fails in the intuitionistic
logic of constant domains. This result refutes two previously published claims
that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text
thouroughly reworked in terms of notation and style, historical notes as well
as some other minor details adde
Theorem proving support in programming language semantics
We describe several views of the semantics of a simple programming language
as formal documents in the calculus of inductive constructions that can be
verified by the Coq proof system. Covered aspects are natural semantics,
denotational semantics, axiomatic semantics, and abstract interpretation.
Descriptions as recursive functions are also provided whenever suitable, thus
yielding a a verification condition generator and a static analyser that can be
run inside the theorem prover for use in reflective proofs. Extraction of an
interpreter from the denotational semantics is also described. All different
aspects are formally proved sound with respect to the natural semantics
specification.Comment: Propos\'e pour publication dans l'ouvrage \`a la m\'emoire de Gilles
Kah
Failure of interpolation in the intuitionistic logic of constant domains
This paper shows that the interpolation theorem fails in the intuitionistic
logic of constant domains. This result refutes two previously published claims
that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text
thouroughly reworked in terms of notation and style, historical notes as well
as some other minor details adde
On axiomatization of Łukasiewicz's four-valued modal logic
Formal aspects of various ways of description of Jan Łukasiewicz’s four-valued modal logic £ are discussed. The original Łukasiewicz’s description by means of the accepted and rejected theorems, together with the four-valued matrix, is presented. Then the improved E.J. Lemmon’s description based upon three specific axioms, together with the relational semantics, is presented as well. It is proved that Lemmon’s axiomatic is not independent: one axiom is derivable on the base of the remanent two. Several axiomatizations, based on three, two or one single axiom are provided and discussed, including S. Kripke’s axiomatics. It is claimed that (a) all substitutions of classical theorems, (b) the rule of modus ponens, (c) the definition of “◊” and (d) the single specific axiom schema: ⬜A ∧ B → A ∧ ⬜B, called the jumping necessity axiom, constitute an elegant axiomatics of the system £
On Constructive Axiomatic Method
In this last version of the paper one may find a critical overview of some
recent philosophical literature on Axiomatic Method and Genetic Method.Comment: 25 pages, no figure
Implicit complexity for coinductive data: a characterization of corecurrence
We propose a framework for reasoning about programs that manipulate
coinductive data as well as inductive data. Our approach is based on using
equational programs, which support a seamless combination of computation and
reasoning, and using productivity (fairness) as the fundamental assertion,
rather than bi-simulation. The latter is expressible in terms of the former. As
an application to this framework, we give an implicit characterization of
corecurrence: a function is definable using corecurrence iff its productivity
is provable using coinduction for formulas in which data-predicates do not
occur negatively. This is an analog, albeit in weaker form, of a
characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar
induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034
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