Related papers: Reasoning about Social Choice and Games in Monadic…
We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been…
A graph class $\mathscr{C}$ is called monadically stable if one cannot interpret, in first-order logic, arbitrary large linear orders in colored graphs from $\mathscr{C}$. We prove that the model checking problem for first-order logic is…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
Purpose: We propose a model to present a possible mechanism for obtaining sizeable behavioural structures by simulating an agent based on the evolutionary public good game with available social learning. Methods: The model considered a…
We show that, in large population games, decentralized information aggregation generically corrects for individual-level biases. This establishes a new testable aggregate efficiency benchmark where the behavior of boundedly rational agents…
Imitation is fundamental in the understanding of social system dynamics. But the diversity of imitation rules employed by modelers proves that the modeling of mimetic processes cannot avoid the traditional problem of endogenization of all…
We show that over the class of linear orders with additional binary relations satisfying some monotonicity conditions, monadic first-order logic has the three-variable property. This generalizes (and gives a new proof of) several known…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…
Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its…
Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Logit dynamics are dynamical systems describing transitions and equilibria of actions of interacting players under uncertainty. An uncertainty is embodied in logit dynamic as a softmax type function often called a logit function originating…
Monotonicity reasoning is one of the important reasoning skills for any intelligent natural language inference (NLI) model in that it requires the ability to capture the interaction between lexical and syntactic structures. Since no test…
Multi-behavior recommendation predicts items a user may purchase by analyzing diverse behaviors like viewing, adding to a cart, and purchasing. Existing methods fall into two categories: representation learning and graph ranking.…
This paper presents an extension of temporal epistemic logic with operators that quantify over agent strategies. Unlike previous work on alternating temporal epistemic logic, the semantics works with systems whose states explicitly encode…
While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…
We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known…