Extensions of first order logic
Extensions of first order logic
A shorter model theory
A Short Introduction to Computational Social Choice
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Computer-aided proofs of Arrow's and other impossibility theorems
Artificial Intelligence
First-order logic formalisation of Arrow's theorem
LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
On the logic of preference and judgment aggregation
Autonomous Agents and Multi-Agent Systems
Computer-aided theorem discovery---a new adventure and its application to economic theory
Computer-aided theorem discovery---a new adventure and its application to economic theory
Discovering theorems in game theory: Two-person games with unique pure Nash equilibrium payoffs
Artificial Intelligence
Applications of logic in social choice theory
CLIMA'11 Proceedings of the 12th international conference on Computational logic in multi-agent systems
A qualitative comparison of the suitability of four theorem provers for basic auction theory
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
The ForMaRE project: formal mathematical reasoning in economics
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision making under uncertainty, is how to extend an agent's preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.