13,965 research outputs found
Understanding game semantics through coherence spaces
AbstractGame Semantics has successfully provided fully abstract models for a variety of programming languages not possible using other denotational approaches. Although it is a flexible and accurate way to give semantics to a language, its underlying mathematics is awkward. For example, the proofs that strategies compose associatively and maintain properties imposed on them such as innocence are intricate and require a lot of attention. This work aims at beginning to provide a more elegant and uniform mathematical ground for Game Semantics. Our quest is to find mathematical entities that will retain the properties that make games an accurate way to give semantics to programs, yet that are simple and familiar to work with. Our main result is a full, faithful strong monoidal embedding of a category of games into a category of coherence spaces, where composition is simple composition of relations
Non uniform (hyper/multi)coherence spaces
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs.
Intuitively, vertices represent results of computations and the edge relation
witnesses the ability of being assembled into a same piece of data or a same
(strongly) stable function, at arrow types. In (hyper)coherence semantics, the
argument of a (strongly) stable functional is always a (strongly) stable
function. As a consequence, comparatively to the relational semantics, where
there is no edge relation, some vertices are missing. Recovering these vertices
is essential for the purpose of reconstructing proofs/terms from their
interpretations. It shall also be useful for the comparison with other
semantics, like game semantics. In [BE01], Bucciarelli and Ehrhard introduced a
so called non uniform coherence space semantics where no vertex is missing. By
constructing the co-free exponential we set a new version of this last
semantics, together with non uniform versions of hypercoherences and
multicoherences, a new semantics where an edge is a finite multiset. Thanks to
the co-free construction, these non uniform semantics are deterministic in the
sense that the intersection of a clique and of an anti-clique contains at most
one vertex, a result of interaction, and extensionally collapse onto the
corresponding uniform semantics.Comment: 32 page
Standard State Space Models of Unawareness
The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate
that standard state-space models cannot be used to represent unawareness. We first show that Dekel,
Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness,
and argue that although one of them may not be adequately modeled using standard state spaces,
there is no reason to think that standard state spaces cannot provide models of the other two notions.
In fact, standard space models of these forms of awareness are attractively simple. They allow us
to prove completeness and decidability results with ease, to carry over standard techniques from
decision theory, and to add propositional quantifiers straightforwardly
In Search of Effectful Dependent Types
Real world programming languages crucially depend on the availability of
computational effects to achieve programming convenience and expressive power
as well as program efficiency. Logical frameworks rely on predicates, or
dependent types, to express detailed logical properties about entities.
According to the Curry-Howard correspondence, programming languages and logical
frameworks should be very closely related. However, a language that has both
good support for real programming and serious proving is still missing from the
programming languages zoo. We believe this is due to a fundamental lack of
understanding of how dependent types should interact with computational
effects. In this thesis, we make a contribution towards such an understanding,
with a focus on semantic methods.Comment: PhD thesis, Version submitted to Exam School
Genetic Action Trees A New Concept for Social and Economic Simulation
Multi-Agent Based Simulation is a branch of Distributed Artificial Intelligence that builds the base for computer simulations which connect the micro and macro level of social and economic scenarios. This paper presents a new method of modelling the formation and change of patterns of action in social systems with the help of Multi-Agent Simulations. The approach is based on two scientific concepts: Genetic Algorithms [Goldberg 1989, Holland 1975] and the theory of Action Trees [Goldman 1971]. Genetic Algorithms were developed following the biological mechanisms of evolution. Action Trees are used in analytic philosophy for the structural description of actions. The theory of Action Trees makes use of the observation of linguistic analysis that through the preposition by a semi-order is induced on a set of actions. Through the application of Genetic Algorithms on the attributes of the actions of an Action Tree an intuitively simple algorithm can be developed with which one can describe the learning behaviour of agents and the changes in action spaces. Using the extremely simplified economic action space, in this paper called “SMALLWORLDâ€, it is shown with the aid of this method how simulated agents react to the qualities and changes of their environment. Thus, one manages to endogenously evoke intuitively comprehensible changes in the agents‘ actions. This way, one can observe in these simulations that the agents move from a barter to a monetary economy because of the higher effectiveness or that they change their behaviour towards actions of fraud.Multi agent system, genetic algorithms, actiontrees, learning, decision making, economic and social behaviour, distributed artificial intelligence
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