Iterative voting allows a group of agents to take a collective decision in a dynamic fashion: a series of plurality elections are staged, making the relative scores of the candidates public after each round. Voters can thus adjust their ballots at each step until the process converges (or a maximal number of steps is reached). Research in computational social choice has shown that this method has the potential of reaching good-quality decisions while at the same time being easy to explain to voters. This paper presents our implementation of iterative voting on a voting platform accessible on the web.

Abstract The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$ , recently shown to be decidable by Fernández-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.

Abstract The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional programming languages with new features via type theory, while from the semantics perspective, several logics for reasoning about dynamical systems and several semantics for logic programming have their roots in this framework. We consider several axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. We provide two distinct interpretations of “henceforth”, both of which are natural intuitionistic variants of the classical one. We completely establish the order relation between the semantically defined logics based on both interpretations of “henceforth” and, using our soundness results, show that the axiomatically defined logics enjoy the same order relations.

We consider intuitionistic variants of linear temporal logic with “next,” “until,” and “release” based on expanding posets : partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic that we denote ITL e , and by imposing additional constraints, we obtain the logics ITL p of persistent posets and ITL ht of here-and-there temporal logic, both of which have been considered in the literature. We prove that ITL e has the effective finite model property and hence is decidable, while ITL p does not have the finite model property. We also introduce notions of bounded bisimulations for these logics and use them to show that the “until” and “release” operators are not definable in terms of each other, even over the class of persistent posets.

We devote this article to the axiomatization/completeness of PRSPDL0 —a variant of iteration-free PDL with parallel composition. Our results are based on the following: although the program operation of parallel composition is not modally definable in the ordinary language of PDL , it becomes definable in a modal language strengthened by the introduction of propositional quantifiers. Instead of using axioms to define the program operation of parallel composition in the language of PDL enlarged with propositional quantifiers, we add an unorthodox rule of proof that makes the canonical model standard for the program operation of parallel composition and we use large programs for the proof of the Truth Lemma.

A new family of modal logics with an associative binary modality, called counting logics is proposed. These propositional logics allow to express finite cardinalities of sets and more generally to count the number of subsets satisfying some properties. We show that these logics can be seen both as specializations of the Boolean logic of bunched implications and as generalizations of the propositional dependence logic. Moreover, whereas most logics with an associative binary modality are undecidable, we prove that some counting logics are decidable, in particular the basic counting logic bCL. We conjecture that this interesting result is due to the valuation constraints in counting logics' semantics and prove that the logic corresponding to bCL without these constraints is undecidable. Finally, we give lower and upper bounds for the complexity of bCL's validity problem.

We introduce the logic ITL^e, an intuitionistic temporal logic based on structures (W,R,S), where R is used to interpret intuitionistic implication and S is an R-monotone function used to interpret temporal modalities. Our main result is that the satisfiability and validity problems for ITL^e are decidable. We prove this by showing that the logic enjoys the strong finite model property. In contrast, we also consider a 'persistent' version of the logic, ITL^p, whose models are similar to Cartesian products. We prove that, unlike ITL^e, ITL^p does not have the finite model property.