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Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.

Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Hey ting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke semantics.

In this paper we examine the mechanism of DeLP (Defeasible Logic Programming). We first study the definition of the defeating relation in a formal setting that allows us to uncover some hidden assumptions, and suggest an alternative definition. Then we introduce a game-theoretic characterization of the system. We obtain a new set of truth values arising from games in which arguments for and against a given literal are played out. We study how additional constraints define protocols of admissible attacks. The DeLP protocol ensures the finiteness of the games, and therefore the existence of winning strategies for the corresponding games. The defeating relation among arguments determines the strategies that will win and consequently the truth values of queries. We find that the DeLP protocol also excludes the warranting of a literal and its negation.

We present a category equivalent to that of semi-Nelson algebras. The objects in this category are pairs consisting of a semi-Heyting algebra and one of its filters. The filters must contain all the dense elements of the semi-Heyting algebra and satisfy an additional technical condition. We also show that the category of dually hemimorphic semi-Nelson algebras is equivalent to that of dually hemimorphic semi-Heyting algebras.

The purpose of this note is to work out the details of the concrete incarnation of a few categorical constructions (products, coproducts, pullbacks, pushouts, equalizers, coequalizers, and exponentials) in some useful and basic categories: the categories of sets, sets endowed with a binary relation, preorders, and posets.

Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players \\(Gam_I\\) is built from this representation, and a more general category \\(Gam\\) is defined with games having different sets of players, both being complete and cocomplete. The notion of Nash equilibrium can be generalized in this context. We then introduce two subcategories of \\(Gam\\), \\(NE\\) and \\(Gam^NE\\) in which the morphisms are equilibria-preserving. We illustrate the expressivity and usefulness of this framework with some examples.

In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures, finitely additive probability measures, plausibilty measures (and their duals, belief functions), and possibility measures. We give axioms and inference rules for the associated system of coalgebraic modal logic, and construct the canonical coalgebras to prove a completeness result.

Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players \\(Gam_I\\) is built from this representation, and a more general category \\(Gam\\) is defined with games having different sets of players, both being complete and cocomplete. The notion of Nash equilibrium can be generalized in this context. We then introduce two subcategories of \\(Gam\\), \\(NE\\) and \\(Gam^NE\\) in which the morphisms are equilibria-preserving. We illustrate the expressivity and usefulness of this framework with some examples.

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to define partial symmetries in payoff matrices. With this purpose, we introduce the notion of the role a player plays with respect to another one, and combinatorial relations between roles are studied. Building on them, we define relations directly between players, which provide yet another characterization of structural symmetries in the payoff matrices of strategic games.

We present a formal analysis of Douglas Hofstadter's concept of superrationality. We start by defining superrationally justifiable actions, and study them in symmetric games. We then model the beliefs of the players, in a way that leads them to different choices than the usual assumption of rationality by restricting the range of conceivable choices. These beliefs are captured in the formal notion of type drawn from epistemic game theory. The theory of coalgebras is used to frame type spaces and to account for the existence of some of them. We find conditions that guarantee superrational outcomes.