Relation-Changing Logics as Fragments of Hybrid Logics

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add, and swap edges in the model, both locally and globally. We provide translations from these logics to hybrid logic along with an implementation. In general, these logics are undecidable, but we use our translations to identify decidable fragments. We also compare the expressive power of relation-changing modal logics with hybrid logics.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Relation-changing modal operators

We study dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements of the domain. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of classical logics. Then, we use the new framework to get a suitable notion of bisimulation for the logics introduced, and we investigate their expressive power. Finally, we show that the complexity of the model checking problem for the particular operators introduced is PSpace-complete, and we study two subproblems of model checking: formula complexity and program complexity.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Satisfiability for relation-changing logics

Relation-changing modal logics (RC for short) are extensions of the basic modal logic with dynamic operators that modify the accessibility relation of a model during the evaluation of a formula. These languages are equipped with dynamic modalities that are able e.g. to delete, add and swap edges in the model, both locally and globally. We study the satisfiability problem for some of these logics.We first show that they can be translated into hybrid logic. As a result, we can transfer some results from hybrid logics to RC. We discuss in particular decidability for some fragments. We then show that satisfiability is, in general, undecidable for all the languages introduced, via translations from memory logics.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martel, Mauricio. Universitat Bremen; Alemani

Imperative change and obligation to do

The ambition of the paper is to provide a solution to the problem posed by Von Wright (1999): how is it possible that the two actions, one of producing P and the other of preventing P can have different deontic status, the former being obligatory and the latter being forbidden. The solution for the problem is sought for by an investigation into connections between imperative and deontic logic. First, it is asked whether a solution could be found in Lemmon's (1965) system of "change logic", using his idea on connection between logic of orders being in force and deontic logic. The answer is the negative one. Next, the connection between Lemmon's imperative logic and deontic logic given in Aqvist's paper - "Next" and "Ought" (1965) - is analyzed. Than, the Lemmon's treatment of imperatives is restricted to the natural language imperatives and Aqvist's way of connecting imperative and deontic logic is modified accordingly. Some principles for the natural language imperatives are established (the negation rule ; the law of contraposition for imperative conditionals) and a simple "global" semantics is developed. The notion of "opposite action" is introduced and it is given an important role in semantics. Finally, a solution for von Wright's problem is given. In the closing sections some further topics for investigation are hinted: one of them being the connection between Aqvist's epistemic- imperative conception of interrogatives and "epistemic obligations", the other being formalization of the idea that imperatives create and re-create obligation patterns that can be described in deontic terms

Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract

In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker's core insights, and using frameworks developed by Bjorndahl and Baltag et al., we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and (roughly speaking) what is knowable; we argue that the foundational axioms of Stalnaker's system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an "evidence-in-hand" conception of knowledge and a weaker "evidence-out-there" notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker's postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.Comment: In Proceedings TARK 2017, arXiv:1707.08250. The full version of this paper, including the longer proofs, is at arXiv:1612.0205

Neurons and symbols: a manifesto

We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty