scholarly journals Games and full completeness for multiplicative linear logic

1994 ◽  
Vol 59 (2) ◽  
pp. 543-574 ◽  
Author(s):  
Samson Abramsky ◽  
Radha Jagadeesan
Keyword(s):  
Linear Logic ◽  
Winning Strategy ◽  
Game Semantics ◽  
Categorical Model ◽  
Natural Notion ◽  
Winning Strategies

AbstractWe 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.

scholarly journals Maker–Breaker percolation games I: crossing grids

2020 ◽  
pp. 1-28
Author(s):  
A. Nicholas Day ◽  
Victor Falgas-Ravry
Keyword(s):  
Percolation Theory ◽  
Winning Strategy ◽  
List Type ◽  
Rectangular Grid ◽  
Grid Graph ◽  
Left Hand ◽  
Right Hand ◽  
Winning Strategies ◽  
Special Case ◽  
Switching Game

Abstract Motivated by problems in percolation theory, we study the following two-player positional game. Let Λm×n be a rectangular grid-graph with m vertices in each row and n vertices in each column. Two players, Maker and Breaker, play in alternating turns. On each of her turns, Maker claims p (as yet unclaimed) edges of the board Λm×n, while on each of his turns Breaker claims q (as yet unclaimed) edges of the board and destroys them. Maker wins the game if she manages to claim all the edges of a crossing path joining the left-hand side of the board to its right-hand side, otherwise Breaker wins. We call this game the (p, q)-crossing game on Λm×n. Given m, n ∈ ℕ, for which pairs (p, q) does Maker have a winning strategy for the (p, q)-crossing game on Λm×n? The (1, 1)-case corresponds exactly to the popular game of Bridg-it, which is well understood due to it being a special case of the older Shannon switching game. In this paper we study the general (p, q)-case. Our main result is to establish the following transition. If p ≥ 2q, then Maker wins the game on arbitrarily long versions of the narrowest board possible, that is, Maker has a winning strategy for the (2q, q)-crossing game on Λm×(q+1) for any m ∈ ℕ. If p ≤ 2q − 1, then for every width n of the board, Breaker has a winning strategy for the (p, q)-crossing game on Λm×n for all sufficiently large board-lengths m. Our winning strategies in both cases adapt more generally to other grids and crossing games. In addition we pose many new questions and problems.

A parallel game semantics for Linear Logic

1997 ◽  
Vol 36 (3) ◽  
pp. 189-217
Author(s):  
Stefano Baratella ◽  
Stefano Berardi
Keyword(s):  
Linear Logic ◽  
Game Semantics

scholarly journals A categorical model of predicate linear logic

2015 ◽  
Vol 14 (1) ◽  
pp. 27-42 ◽  
Author(s):  
Emilia Demeterova ◽  
◽  
Daniel Mihalyi ◽  
Valerie Novitzka ◽  
◽  
...  
Keyword(s):  
Linear Logic ◽  
Categorical Model

scholarly journals Strategi Pemenangan Pasangan Calon Herman Deru Dan Mawardi Yahya Pada Pilkada Sumatera Selatan Tahun 2018

2019 ◽  
Vol 3 (1) ◽  
pp. 17-27
Author(s):  
Maharani Maharani
Keyword(s):  
Winning Strategy ◽  
Descriptive Study ◽  
Organizational Strategy ◽  
The South ◽  
Program Strategy ◽  
Institutional Strategy ◽  
Public Debates ◽  
Winning Strategies ◽  
Qualitative Descriptive ◽  
The Media

Election of Regional Heads of South Sumatra Province has been held in 2018 with 4 pairs of candidates participated and won by the couple Herman Deru and Mawardi Yahya. The interesting thing from this research is that there has been intense competition between the four Paslon. Where each candidate, previously served as regional head in several districts in South Sumatra. The victory of this couple did not escape the winning strategy that they have implemented. The problem discussed in this study is how the process of the campaign implemented by Herman Deru and Mawardi Yahya in the South Sumatra Regional Election in 2018 and what the winning strategy used by the Paslon. The researcher uses the strategy theory from Kotten where in this theory it is stated that there are 4 types of winning strategies namely organizational strategy, program strategy, resource strategy, and institutional strategy. This type of research is a qualitative descriptive study. Methods of collecting data from this study through interviews, observation, and documentation. The results of this study indicate that of the 4 types of winning strategies as proposed by Kotten, the four strategies have been implemented by the couple Herman Deru and Mawardi Yahya. The strategy they use is different from the strategies used by other partners such as organizational strategy. Specifically in the program section and how to campaign through social media. And there are 4 stages of the campaign process set by the South Sumatra KPU in the South Sumatra Regional Election in the 2018-2023 period, namely public debates, distribution of campaign materials, installation of campaign props, and campaign advertisements in the media.

scholarly journals Preface

2016 ◽  
Vol 28 (7) ◽  
pp. 991-994
Author(s):  
LORENZO TORTORA DE FALCO
Keyword(s):  
Taylor Expansion ◽  
Linear Logic ◽  
Research Area ◽  
Theoretical Computer Science ◽  
Quantitative Approach ◽  
Algebraic Setting ◽  
Use Of Resources ◽  
Natural Notion ◽  
Proof Nets ◽  
New Ideas

This special issue is devoted to some aspects of the new ideas that recently arose from the work of Thomas Ehrhard on the models of linear logic (LL) and of the λ-calculus. In some sense, the very origin of these ideas dates back to the introduction of LL in the 80s by Jean-Yves Girard. An obvious remark is that LL yielded a first logical quantitative account of the use of resources: the logical distinction between linear and non-linear formulas through the introduction of the exponential connectives. As explicitly mentioned by Girard in his first paper on the subject, the quantitative approach, to which he refers as ‘quantitative semantics,’ had a crucial influence on the birth of LL. And even though, at that time, it was given up for lack of ‘any logical justification’ (quoting the author), it contained rough versions of many concepts that were better understood, precisely introduced and developed much later, like differentiation and Taylor expansion for proofs. Around 2003, and thanks to the developments of LL and of the whole research area between logic and theoretical computer science, Ehrhard could come back to these fundamental intuitions and introduce the structure of finiteness space, allowing to reformulate this quantitative approach in a standard algebraic setting. The interpretation of LL in the category Fin of finiteness spaces and finitary relations suggested to Ehrhard and Regnier the differential extensions of LL and of the simply typed λ-calculus: Differential Linear Logic (DiLL) and the differential λ-calculus. The theory of LL proof-nets could be straightforwardly extended to DiLL, and a very natural notion of Taylor expansion of a proof-net (and of a λ-term) was introduced: an element of the Taylor expansion of the proof-net/term α is itself a (differential) proof-net/term and an approximation of α.

scholarly journals A linear category of polynomial diagrams

2013 ◽  
Vol 24 (1) ◽  
Author(s):  
PIERRE HYVERNAT
Keyword(s):  
Tensor Product ◽  
Linear Logic ◽  
Structure Tensor ◽  
Multiplicative Structure ◽  
Cartesian Closed Category ◽  
Closed Category ◽  
Categorical Model ◽  
Cartesian Closed ◽  
Linear Category ◽  
Intuitionistic Linear Logic

We present a categorical model for intuitionistic linear logic in which objects are polynomial diagrams and morphisms aresimulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally cartesian closed category, but the additive (product and coproduct) and exponential (-comonoid comonad) structures require additional properties and are only developed in the categorySet, where the objects and morphisms have natural interpretations in terms of games, simulation and strategies.

scholarly journals Abstract classes with few models have ‘homogeneous-universal’ models

1995 ◽  
Vol 60 (1) ◽  
pp. 246-265 ◽  
Author(s):  
J. Baldwin ◽  
S. Shelah
Keyword(s):  
Amalgamation Property ◽  
Prime Model ◽  
Universal Model ◽  
Natural Notion ◽  
Winning Strategies ◽  
Universal Domain ◽  
Abstract Notion ◽  
Normal Sense ◽  
Weak Extension

This paper is concerned with a class K of models and an abstract notion of submodel ≤. Experience in first order model theory has shown the desirability of finding a ‘monster model’ to serve as a universal domain for K. In the original constructions of Jónsson and Fraïssé, K was a universal class and ordinary substructure played the role of ≤. Working with a cardinal λ satisfying λ<λ = λ guarantees appropriate downward Löwenheim-Skolem theorems; the existence and uniqueness of a homogeneous-universal model appears to depend centrally on the amalgamation property. We make this apparent dependence more precise in this paper.The major innovation of this paper is the introduction of a weaker notion (chain homogeneous-universal) to replace the natural notion of (K, <)-homogeneous-universal model. Modulo a weak extension of ZFC (provable if V = L), we show (Corollary 5.24) that a class K obeying certain minimal restrictions satisfies a fundamental dichotomy. For arbitrarily large λ, either K has the maximal number of models in power λ or K has a unique chain homogeneous-universal model of power λ. We show (5.25) in a class with amalgamation this dichotomy holds for the notion of K-homogeneous-universal model in the more normal sense.The methods here allow us to improve our earlier results [5] in two other ways: certain requirements on all chains of a given length are replaced by requiring winning strategies in certain games; the notion of a canonically prime model is avoided. A full understanding of these extensions requires consideration of the earlier papers but we summarize them quickly here.

scholarly journals A game semantics for linear logic

1992 ◽  
Vol 56 (1-3) ◽  
pp. 183-220 ◽  
Author(s):  
Andreas Blass
Keyword(s):  
Linear Logic ◽  
Game Semantics

scholarly journals Political Contestation of Hindu Legislative Candidates in the 2019 Election in Nusa Tenggara Barat

2020 ◽  
Vol 36 (2) ◽  
Author(s):  
Susilo Edi Purwanto
Keyword(s):  
Social Media ◽  
Data Analysis ◽  
Winning Strategy ◽  
Qualitative Approach ◽  
Data Display ◽  
Structured Interviews ◽  
Self Actualization ◽  
Collection Data ◽  
Personal Approach ◽  
Winning Strategies

This study aims to describe the motivation and winning strategies of Hindu legislative candidates in political participation, especially in the province of Nusa Tenggara Barat (NTB). This study is conducted under a qualitative approach whereby the data are collected using observation, documentation, and semi-structured interviews. The Miles and Huberman models are used in the data analysis including data collection, data reduction, data display, and data conclusion. The results of the study suggested that the participation of Hindu candidates in NTB in the 2019 election contestation has various motivations such as physiological, security, belongingness and love, appreciation, and self-actualization needs. Also, the winning strategy for both incumbent and newcomer groups is carried out almost the same, namely by conducting socialization using media posters, billboards, banners, stickers, and also social media to promote the profile of candidates. Apart from that, a personal approach is also done by directly come to the community and talk to them personally to win their hearts

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