37,998 research outputs found
Constructive Hybrid Games
Hybrid games are models which combine discrete, continuous, and adversarial
dynamics. Game logic enables proving (classical) existence of winning
strategies. We introduce constructive differential game logic (CdGL) for hybrid
games, where proofs that a player can win the game correspond to computable
winning strategies. This is the logical foundation for synthesis of correct
control and monitoring code for safety-critical cyber-physical systems. Our
contributions include novel static and dynamic semantics as well as soundness
and consistency.Comment: 60 pages, preprint, under revie
From truth to computability II
Computability logic is a formal theory of computational tasks and resources.
Formulas in it represent interactive computational problems, and "truth" is
understood as algorithmic solvability. Interactive computational problems, in
turn, are defined as a certain sort games between a machine and its
environment, with logical operators standing for operations on such games.
Within the ambitious program of finding axiomatizations for incrementally rich
fragments of this semantically introduced logic, the earlier article "From
truth to computability I" proved soundness and completeness for system CL3,
whose language has the so called parallel connectives (including negation),
choice connectives, choice quantifiers, and blind quantifiers. The present
paper extends that result to the significantly more expressive system CL4 with
the same collection of logical operators. What makes CL4 expressive is the
presence of two sorts of atoms in its language: elementary atoms, representing
elementary computational problems (i.e. predicates, i.e. problems of zero
degree of interactivity), and general atoms, representing arbitrary
computational problems. CL4 conservatively extends CL3, with the latter being
nothing but the general-atom-free fragment of the former. Removing the blind
(classical) group of quantifiers from the language of CL4 is shown to yield a
decidable logic despite the fact that the latter is still first-order. A
comprehensive online source on computability logic can be found at
http://www.cis.upenn.edu/~giorgi/cl.htm
Ptarithmetic
The present article introduces ptarithmetic (short for "polynomial time
arithmetic") -- a formal number theory similar to the well known Peano
arithmetic, but based on the recently born computability logic (see
http://www.cis.upenn.edu/~giorgi/cl.html) instead of classical logic. The
formulas of ptarithmetic represent interactive computational problems rather
than just true/false statements, and their "truth" is understood as existence
of a polynomial time solution. The system of ptarithmetic elaborated in this
article is shown to be sound and complete. Sound in the sense that every
theorem T of the system represents an interactive number-theoretic
computational problem with a polynomial time solution and, furthermore, such a
solution can be effectively extracted from a proof of T. And complete in the
sense that every interactive number-theoretic problem with a polynomial time
solution is represented by some theorem T of the system.
The paper is self-contained, and can be read without any previous familiarity
with computability logic.Comment: Substantially better versions are on their way. Hence the present
article probably will not be publishe
Supply chains : ago-antagonistic systems through co-opetition game theory lens
Supply chain configurations, as hybrid governance structures, allow companies to be sufficiently integrated while keeping a certain level of flexibility. This enables them, on one hand, to converge towards common interests through the development of cooperation; and on the other hand, to diverge on their own interests by remaining in competition. This dynamics generates an ago-antagonistic system where both of these two concepts, namely cooperation and competition, simultaneously drive the supply chain. In the present article, this system is analyzed by using the co-opetition game theory developed by Brandenburger and Nalebuff (1996) in order to highlight the importance of such an apprehension of the supply chain approach.Supply chain; cooperation; competition; ago-antagonistic approach; co-opetition game theory
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