Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Knowledge and Blameworthiness

Blameworthiness of an agent or a coalition of agents is often defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should have had a strategy to prevent it. In this article we argue that in the settings with imperfect information, not only should the coalition have had a strategy, but it also should have known that it had a strategy, and it should have known what the strategy was. The main technical result of the article is a sound and complete bimodal logic that describes the interplay between knowledge and blameworthiness in strategic games with imperfect information

On Fibring Semantics for BDI Logics

This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing (a special form of fibring) can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema G^[a, b, c, d]. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having a fibred approach is discussed in the final section

A Fibred Tableau Calculus for BDI Logics

In [12,16] we showed how to combine propositional BDI logics using Gabbay's fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based decision procedure for the combined/fibred logics. To achieve this end we first outline with an example two types of tableau systems, (graph and path), and discuss why both are inadequate in the case of fibring. Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system KEM

Well-orders in the transfinite Japaridze algebra

This paper studies the transfinite propositional provability logics \glp_\Lambda and their corresponding algebras. These logics have for each ordinal $\xi< \Lambda$ a modality \la \alpha \ra. We will focus on the closed fragment of \glp_\Lambda (i.e., where no propositional variables occur) and \emph{worms} therein. Worms are iterated consistency expressions of the form \la \xi_n\ra \ldots \la \xi_1 \ra \top. Beklemishev has defined well-orderings $<_\xi$ on worms whose modalities are all at least $\xi$ and presented a calculus to compute the respective order-types. In the current paper we present a generalization of the original $<_\xi$ orderings and provide a calculus for the corresponding generalized order-types $o_\xi$. Our calculus is based on so-called {\em hyperations} which are transfinite iterations of normal functions. Finally, we give two different characterizations of those sequences of ordinals which are of the form \la {\formerOmega}_\xi (A) \ra_{\xi \in \ord} for some worm $A$. One of these characterizations is in terms of a second kind of transfinite iteration called {\em cohyperation.}Comment: Corrected a minor but confusing omission in the relation between Veblen progressions and hyperation

Embodied Cognition. Body, movement and sport for didactics

Embodied Cognition (EC) is an interdisciplinary and multiperspective scientific theory whose characteristic, from a cultural and professional perspective, opens up interesting scenarios in the field of psychopedagogy. In particular, a prolific and extremely interesting area of study is now provided by the contribution of EC to the world of didactics (Caruana &amp; Borghi, 2013). This work is part of this research horizon, investigating how the key principles of Embodied Cognition offer new opportunities to enhance differences in learning processes (Gomez Paloma &amp; Ianes, a cura di, 2014). Starting from the analysis of the body as a scientific mediator of the learning process on a neurobiological (Rizzolatti &amp; Sinigaglia, 2006) and neurophenomenological (Gallese, 2006) level, the study focuses on the scientific evidence (Margiotta, 2014) that EC can provide to teachers in the field of didactics. It represents a concrete springboard for delineating and validating an “EC-Based” model (Gomez Paloma &amp; Damiani, 2015) to enhance corporeality as a cognitive system and a learning/ contextualization setting for the building of professional skills in the field of education

Embodied Cognition Corpo, movimento e sport per la didattica

Embodied Cognition (EC) is an interdisciplinary and multiperspective scientific theory whose characteristic, from a cultural and professional perspective, opens up interesting scenarios in the field of psychopedagogy. In particular, a prolific and extremely interesting area of study is now provided by the contribution of EC to the world of didactics (Caruana &amp; Borghi, 2013).This work is part of this research horizon, investigating how the key principles of Embodied Cognition offer new opportunities to enhance differences in learning processes (Gomez Paloma &amp; Ianes, a cura di, 2014). Starting from the analysis of the body as a scientific mediator of the learning process on a neurobiological (Rizzolatti &amp; Sinigaglia, 2006) and neurophenomenological (Gallese, 2006) level, the study focuses on the scientific evidence (Margiotta, 2014) that EC canprovide to teachers in the field of didactics. It represents a concrete springboard for delineating and validating an “EC-Based” model (Gomez Paloma &amp; Damiani, 2015) to enhance corporeality as a cognitive system and a learning/ contextualization setting for the building of professional skills in the fieldof education.L’Embodied Cognition (EC) è una teoria scientifica multiprospettica ed interdisciplinare la cui caratteristica, riflettendo sotto il profilo culturale e professionale, apre interessanti scenari nel campo della psicopedagogia.In particolare, un fertile ambito di studio, estremamente interessante, è dato al momento dall’apporto dell’EC al mondo della didattica (Caruana &amp; Borghi, 2013). Il presente lavoro si inserisce in quest’orizzonte di ricerca, indagando come i principi chiave dell’Embodied Cognition offrano inedite opportunità di valorizzazione delle differenze dei processi di apprendimento (Gomez Paloma &amp; Ianes, a cura di, 2014). Partendo dall’analisi del corpo come mediatorescientifico del processo di apprendimento a livello neurobiologico (Rizzolatti &amp;Sinigaglia, 2006) e neurofenomenologico (Gallese, 2006), lo studio si focalizza sulle evidenze scientifiche (Margiotta, 2014) che l’EC può offrire al docente nell’ambito della didattica. Un concreto trampolino di lancio per delineare e validare un modello “EC Based” (Gomez Paloma &amp; Damiani, 2015) per valorizzare la corporeità come dispositivo cognitivo e come ambiente di apprendimento e contestualizzazione (setting) per la costruzione di competenze professionali nell’ambito della formazione