Using formal tools in computer science to describe games is an interesting problem. We give games, exactly two person games, an axiomatical foundation based on the process algebra ACP (Algebra of Communicating Process). A fresh operator called opponent's alternative composition operator (OA) is introduced into ACP to describe game trees and game strategies, called GameACP. And its sound and complete axiomatical system is naturally established. To model the outcomes of games (the co-action of the player and the opponent), correspondingly in GameACP, the execution of GameACP processes, another operator called playing operator (PO) is extended into GameACP. We also establish a sound and complete axiomatical system for PO. Finally, we give the correctness theorem between the outcomes of games and the deductions of GameACP processes.
Algorithmic game semantics @cite_10 is the premise of implementation of game semantics for further automatic reasoning machine based on some specific game semantics model. And game semantics can be used to establish the so-called interaction semantics @cite_21 among autonomous agents, and can be used to model and verify compositional software @cite_16 @cite_19 .
@cite_19 @cite_21 @cite_10 @cite_16
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A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for Multiplicative-Additive Linear Logic is proved for this semantics. In game semantics, the higher-order value passing mechanisms of the λ-calculus are decomposed as sequences of atomic actions exchanged by a Player and its Opponent. Seen from this angle, game semantics is reminiscent of trace semantics in concurrency theory, where a process is identified to the sequences of requests it generates in the course of time. Asynchronous game semantics is an attempt to bridge the gap between the two subjects, and to see mainstream game semantics as a refined and interactive form of trace semantics. Asynchronous games are positional games played on Mazurkiewicz traces, which reformulate (and generalize) the familiar notion of arena game. The interleaving semantics of λ-terms, expressed as innocent strategies, may be analysed in this framework, in the perspective of true concurrency. The analysis reveals that innocent strategies are positional strategies regulated by forward and backward confluence properties. This captures, we believe, the essence of innocence. We conclude the article by defining a non-uniform variant of the λ-calculus, in which the game semantics of a λ-term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that λ-term. Automatic interpretation of sports games is a major challenge, especially when these sports feature complex players organizations and game phases. This paper describes a bottom-up approach based on the extraction of semantic features from the video stream of the main camera in the particular case of soccer using scene-specific techniques. In our approach, all the features, ranging from the pixel level to the game event level, have a semantic meaning. First, we design our own scene-specific deep learning semantic segmentation network and hue histogram analysis to extract pixel-level semantics for the field, players, and lines. These pixel-level semantics are then processed to compute interpretative semantic features which represent characteristics of the game in the video stream that are exploited to interpret soccer. For example, they correspond to how players are distributed in the image or the part of the field that is filmed. Finally, we show how these interpretative semantic features can be used to set up and train a semantic-based decision tree classifier for major game events with a restricted amount of training data. The main advantages of our semantic approach are that it only requires the video feed of the main camera to extract the semantic features, with no need for camera calibration, field homography, player tracking, or ball position estimation. While the automatic interpretation of sports games remains challenging, our approach allows us to achieve promising results for the semantic feature extraction and for the classification between major soccer game events such as attack, goal or goal opportunity, defense, and middle game. We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of history-free strategy: strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass, et al