1,721,063 research outputs found
Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information
No full textWe present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies
Upwards closed dependencies in team semantics
No full textWe prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As a consequence, the negations of functional dependence, conditional independence, inclusion and exclusion atoms can all be added to first-order logic without increasing its expressive power. Furthermore, we define a class of bounded upwards closed dependencies and we prove that unbounded dependencies cannot be defined in terms of bounded ones
Doubly strongly first-order dependencies
No full textTeam Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments, called teams. In this semantics, it is possible to add new atoms and connectives expressing dependencies between possible values of variables. Some of the resulting logics are more expressive than first-order logic while others are not. I study the (relativizable) atoms and families of atoms that do not increase the expressive power of first-order logic when they and their complements are added to it, separately or jointly, calling them doubly strongly first-order dependencies and finding a characterization for them
Towards an algebraic approach to theory and concept evaluation
No full textI introduce a theoretical framework for reasoning about the values of theories (understood as sets of elements of random conceptual algebras) and about the values of concepts with respect to theories. Then I define theory formation games and argue that they provide an adequate theoretical framework for the evaluation of strategies and algorithms for computational creativity; and, finally, I briefly discuss two possible practical applications of this framework, namely the automatic search for Natural Deduction rule systems for logics and the construction of falling-rule-list-plus-definitions classification models
Biometrics and artificial creativity
No full textI argue that neither explicit user evaluation nor self-directed exploration of pre-determined spaces of possibilities are viable approaches for implementing artificial systems whose products are recognizable by humans as creative and valuable and, at the same time, as genuinely authored by the artificial system (rather than by the original designer or by the human users): indeed, self-directed creativity requires critical engagement with a creative community, and for now artificial systems are not capable of interacting with human creative communities as peers. I suggest a possible alternative, which might hypothetically be used to grant some degree of authorship to artificial systems without having general artificial intelligence as a prerequisite: in brief, artificial systems could be trained, through the use of biometrics, to generate products that induce the same types of reactions in humans of recognized creative works. As this would not draw conscious human decision-making into the production process, there would then be grounds to argue that the products of such a system would have indeed non-human authorship
Strongly First Order Disjunctive Embedded Dependencies in Team Semantics
No full textFirst Order Team Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments. In Team Semantics, it is possible to extend First Order Logic via new types of atoms that describe dependencies between variables; some of these extensions are strictly more expressive than First Order Logic, while others are reducible to it. Many of the atoms studied in Team Semantics are inspired by Database Theory and belong in particular to the class of Disjunctive Embedded Dependencies, a very general family of dependencies that contains most of the dependencies of practical interest in the study of databases. In this work, I provide a characterization for the (domain-independent) Disjunctive Embedded Dependencies that fail to increase the expressive power of First-Order Team Semantics when added to it
- …
