Game-theoretic semantics for non-distributive logics

2019 ◽  
Vol 27 (5) ◽  
pp. 718-742
Author(s):  
Chrysafis Hartonas
Keyword(s):  
The Other ◽  
Game Playing ◽  
Modal Operators ◽  
Game Theoretic ◽  
Game Theoretic Semantics

AbstractWe introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for the logics of lattices with weak negation and modal operators (Modal Lattice Logic).

which challenges him into interpretative activity, into being a solver and realizer of the text rather than just a passive consumer of it. I have subjected the giraffe to such prolonged analysis because it is an emblematic beast. The point I want to stress in this paper is that Heliodoros’ whole novel demands an active interpretative response from his reader. The Aithioptka is a much more challen­ ging read than any of the other Greek novels, precisely because it is pervaded at every level by the kind of self-conscious game-playing typified by the riddle of the giraffe. Here, for instance, is the Egyptian priest, Kalasiris, who acts as narrator for about a third of the whole novel, describing a dream he had on the island of Zakynthos: as I slept, a vision of an old man appeared to me. Age had withered him almost to a skeleton, except that his cloak was hitched up to reveal a thigh that retained some vestige of the strength of his youth. He wore a leather helmet on his head, and his expression was one of cunning and many wiles; he was lame in one leg, as if from a wound of some kind. (5.22.1) The vision reproaches Kalasiris for failing even to pay him a visit while in the vicinity, prophesies punishment for the omission, but conveys greetings from his wife to Kalasiris’ charge, the heroine Charikleja, ‘since she esteems chastity above all things’ (5.22.3). Again a riddle is set up by not immediately identifying the old man, and again the description is presented from the point of view of a character within the story. Here, however, the situation is rather more complicated, since Kalasiris himself has two aspects, as narrator and character within his own narration. As narrator he knows the identity of the dream figure, but in his presentation of his own experience he omits any explanatory gloss, and re-enacts the perplexity of his initial reaction. He describes the dream as he saw it, rather than as he subsequently understood it. Again the reader is challenged to disambiguate the riddle by matching the points of the description with knowledge acquired elsewhere. Every detail corresponds to something in the Homeric poems.4 This time Heliodoros has succeeded in keeping the easiest clues to the end, particularly the formulaic epithet polytropos (‘of many wiles’), proverbially associated with one epic individual, and the reference to a wound in the leg which also clinches its owner’s recognition in the original. Further clues are offered by the fact

2014 ◽  
pp. 320-320
Keyword(s):  
Point Of View ◽  
The Other ◽  
Initial Reaction ◽  
Game Playing ◽  
Set Up ◽  
As If

scholarly journals Game-Theoretic Semantics for Alternating-Time Temporal Logic

2018 ◽  
Vol 19 (3) ◽  
pp. 1-38 ◽  
Author(s):  
Valentin Goranko ◽  
Antti Kuusisto ◽  
Raine Rönnholm
Keyword(s):  
Temporal Logic ◽  
Game Theoretic ◽  
Game Theoretic Semantics

Power-collapsing games

2008 ◽  
Vol 73 (4) ◽  
pp. 1433-1457 ◽  
Author(s):  
Miloš S. Kurilić ◽  
Boris Šobot
Keyword(s):  
Boolean Algebra ◽  
Dense Subset ◽  
Winning Strategy ◽  
Zero Element ◽  
The Other ◽  
Complete Boolean Algebra ◽  
Infinite Cardinal ◽  
Other Hand ◽  
Game Theoretic

AbstractThe game is played on a complete Boolean algebra , by two players. White and Black, in κ-many moves (where κ is an infinite cardinal). At the beginning White chooses a non-zero element p ∈ . In the α-th move White chooses pα ∈ (0, p) and Black responds choosing iα ∈{0, 1}. White winsthe play iff . where and .The corresponding game theoretic properties of c.B.a.'s are investigated. So, Black has a winning strategy (w.s.) if κ ≥ π() or if contains a κ-closed dense subset. On the other hand, if White has a w.s., then κ ∈ . The existence of w.s. is characterized in a combinatorial way and in terms of forcing. In particular, if 2<κ = κ ∈ Reg and forcing by preserves the regularity of κ, then White has a w.s. iff the power 2κ is collapsed to κ in some extension. It is shown that, under the GCH, for each set S ⊆ Reg there is a c.B.a. such that White (respectively. Black) has a w.s. for each infinite cardinal κ ∈ S (resp. κ ∉ S). Also it is shown consistent that for each κ ∈ Reg there is a c.B.a. on which the game is undetermined.

A Formal Model of Learning and Policy Diffusion

2008 ◽  
Vol 102 (3) ◽  
pp. 319-332 ◽  
Author(s):  
CRAIG VOLDEN ◽  
MICHAEL M. TING ◽  
DANIEL P. CARPENTER
Keyword(s):  
Formal Model ◽  
Policy Diffusion ◽  
The Other ◽  
Policy Choice ◽  
Game Theoretic ◽  
Empirical Tests ◽  
The Way

We present a model of learning and policy choice across governments. Governments choose policies with known ideological positions but initially unknown valence benefits, possibly learning about those benefits between the model's two periods. There are two variants of the model; in one, governments only learn from their own experiences, whereas in the other they learn from one another's experiments. Based on similarities between these two versions, we illustrate that much accepted scholarly evidence of policy diffusion could simply have arisen through independent actions by governments that only learn from their own experiences. However, differences between the game-theoretic and decision-theoretic models point the way to future empirical tests that discern learning-based policy diffusion from independent policy adoptions.

scholarly journals LOGICS AND ALGEBRAS FOR MULTIPLE PLAYERS

2010 ◽  
Vol 3 (3) ◽  
pp. 485-519 ◽  
Author(s):  
LOES OLDE LOOHUIS ◽  
YDE VENEMA
Keyword(s):  
Computational Complexity ◽  
Winning Strategy ◽  
Boolean Algebras ◽  
Game Theoretic ◽  
Np Complete ◽  
Game Theoretic Semantics ◽  
Stone’S Theorem

We study a generalization of the standard syntax and game-theoretic semantics of logic, which is based on a duality between two players, to a multiplayer setting. We define propositional and modal languages of multiplayer formulas, and provide them with a semantics involving a multiplayer game. Our focus is on the notion of equivalence between two formulas, which is defined by saying that two formulas are equivalent if under each valuation, the set of players with a winning strategy is the same in the two respective associated games. We provide a derivation system which enumerates the pairs of equivalent formulas, both in the propositional case and in the modal case. Our approach is algebraic: We introduce multiplayer algebras as the analogue of Boolean algebras, and show, as the corresponding analog to Stone’s theorem, that these abstract multiplayer algebras can be represented as concrete ones which capture the game-theoretic semantics. For the modal case we prove a similar result. We also address the computational complexity of the problem whether two given multiplayer formulas are equivalent. In the propositional case, we show that this problem is co-NP-complete, whereas in the modal case, it is PSPACE-hard.

Hobbes's State of Nature: A Modern Bayesian Game-Theoretic Analysis

2015 ◽  
Vol 1 (3) ◽  
pp. 485-508 ◽  
Author(s):  
HUN CHUNG
Keyword(s):  
Game Theory ◽  
The State ◽  
The Other ◽  
Theoretic Model ◽  
Theoretic Analysis ◽  
Bayesian Game ◽  
Game Theoretic Analysis ◽  
State Of Nature ◽  
Game Theoretic ◽  
Game Theoretic Model

ABSTRACT:Hobbes's own justification for the existence of governments relies on the assumption that without a government our lives in the state of nature would result in a state of war of every man against every man. Many contemporary scholars have tried to explain why universal war is unavoidable in Hobbes's state of nature by utilizing modern game theory. However, most game-theoretic models that have been presented so far do not accurately capture what Hobbes deems to be the primary cause of conflict in the state of nature—namely, uncertainty, rather than people's egoistic psychology. Therefore, I claim that any game-theoretic model that does not incorporate uncertainty into the picture is the wrong model. In this paper, I use Bayesian game theory to show how universal conflict can break out in the state of nature—even when the majority of the population would strictly prefer to cooperate and seek peace with other people—due to uncertainty about what type of person the other player is. Along the way, I show that the valuation of one's own life is one of the central mechanisms that drives Hobbes's pessimistic conclusion.

scholarly journals On Partially Controlled Multi-Agent Systems

1996 ◽  
Vol 4 ◽  
pp. 477-507 ◽  
Author(s):  
R. I. Brafman ◽  
M. Tennenholtz
Keyword(s):  
Expected Utility ◽  
The Other ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Direct Control ◽  
Agent System ◽  
Agent Systems ◽  
Multi Agent ◽  
Game Theoretic

Motivated by the control theoretic distinction between controllable and uncontrollable events, we distinguish between two types of agents within a multi-agent system: controllable agents, which are directly controlled by the system's designer, and uncontrollable agents, which are not under the designer's direct control. We refer to such systems as partially controlled multi-agent systems, and we investigate how one might influence the behavior of the uncontrolled agents through appropriate design of the controlled agents. In particular, we wish to understand which problems are naturally described in these terms, what methods can be applied to influence the uncontrollable agents, the effectiveness of such methods, and whether similar methods work across different domains. Using a game-theoretic framework, this paper studies the design of partially controlled multi-agent systems in two contexts: in one context, the uncontrollable agents are expected utility maximizers, while in the other they are reinforcement learners. We suggest different techniques for controlling agents' behavior in each domain, assess their success, and examine their relationship.

scholarly journals Semantics for Hyperclassical Logic and the Problem of Negation in the Formal Language

2018 ◽  
Vol 16 (3) ◽  
pp. 5-15
Author(s):  
V. V. Tselishchev
Keyword(s):  
Theoretical Model ◽  
Formal Language ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Order Language ◽  
Winning Strategies ◽  
Game Theoretic ◽  
Definition Of ◽  
Game Theoretic Semantics

The application of game-theoretic semantics for first-order logic is based on a certain kind of semantic assumptions, directly related to the asymmetry of the definition of truth and lies as the winning strategies of the Verifier (Abelard) and the Counterfeiter (Eloise). This asymmetry becomes apparent when applying GTS to IFL. The legitimacy of applying GTS when it is transferred to IFL is based on the adequacy of GTS for FOL. But this circumstance is not a reason to believe that one can hope for the same adequacy in the case of IFL. Then the question arises if GTS is a natural semantics for IFL. Apparently, the intuitive understanding of negation in natural language can be explicated in formal languages in various ways, and the result of an incomplete grasp of the concept in these languages can be considered a certain kind of anomalies, in view of the apparent simplicity of the explicated concept. Comparison of the theoretical-model and game theoretic semantics in application to two kinds of language – the first-order language and friendly-independent logic – allows to discover the causes of the anomaly and outline ways to overcome it.

scholarly journals Academics at play: Why the “publication game” is more than a metaphor

2020 ◽  
Vol 51 (4) ◽  
pp. 414-430 ◽  
Author(s):  
Nick Butler ◽  
Sverre Spoelstra
Keyword(s):  
Academic Research ◽  
Academic Work ◽  
The Other ◽  
Career Goals ◽  
Game Playing ◽  
Structured Interviews ◽  
Academic Researchers ◽  
Critical Management ◽  
The University ◽  
Meaningful Research

It is increasingly common to describe academic research as a “publication game,” a metaphor that connotes instrumental strategies for publishing in highly rated journals. However, we suggest that the use of this metaphor is problematic. In particular, the metaphor allows scholars to make a convenient, but ultimately misleading, distinction between figurative game-playing on one hand (i.e. pursuing external career goals through instrumental publishing) and proper research on the other hand (i.e. producing intrinsically meaningful research). In other words, the “publication game” implies that while academic researchers may behave just like players, they are not really playing a game. Drawing on semi-structured interviews, we show that this metaphor prevents us, ironically, from fully grasping the lusory attitude, or play-mentality, that characterizes academic work among critical management researchers. Ultimately, we seek to stimulate reflection about how our choice of metaphor can have performative effects in the university and influence our behavior in unforeseen and potentially undesirable ways.

Frenemies in Platform Markets: Heterogeneous Profit Foci as Drivers of Compatibility Decisions

2020 ◽  
Vol 66 (6) ◽  
pp. 2432-2451 ◽  
Author(s):  
Ron Adner ◽  
Jianqing Chen ◽  
Feng Zhu
Keyword(s):  
Information Systems ◽  
Social Welfare ◽  
The Other ◽  
Theoretic Model ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
The Difference

We study compatibility decisions of two competing platform owners that generate profits through both hardware sales and royalties from content sales. We consider a game-theoretic model in which two platforms offer different standalone utilities to users. We find that incentives to establish one-way compatibility—the platform owner with smaller standalone value grants access to its proprietary content application to users of the competing platform—can arise from the difference in their profit foci. As the difference in the standalone utilities increases, royalties from content sales become less important to the platform owner with greater standalone value, but more important to the other platform owner. One-way compatibility can thus increase asymmetry between the platform owners’ profit foci and, given a sufficiently large difference in the standalone utilities, yields greater profits for both platform owners. We further show that social welfare is greater under one-way compatibility than under incompatibility. We also investigate how factors such as exclusive content and hardware-only adopters affect compatibility incentives. This paper was accepted by Chris Forman, information systems.

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