On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus

Cross-domain classification of physical activity intensity: An eda-based approach validated by wrist-measured acceleration and physiological data

Performing regular physical activity positively affects individuals’ quality of life in both the short-and long-term and also contributes to the prevention of chronic diseases. However, exerted effort is subjectively perceived from different individuals. Therefore, this work explores an out-of-laboratory approach using a wrist-worn device to classify the perceived intensity of physical effort based on quantitative measured data. First, the exerted intensity is classified by two machine learning algorithms, namely the Support Vector Machine and the Bagged Tree, fed with features computed on heart-related parameters, skin temperature, and wrist acceleration. Then, the outcomes of the classification are exploited to validate the use of the Electrodermal Activity signal alone to rate the perceived effort. The results show that the Support Vector Machine algorithm applied on physiological and acceleration data effectively predicted the relative physical activity intensities, while the Bagged Tree performed best when the Electrodermal Activity data were the only data used

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

Ecumenical modal logic

The discussion about how to put together Gentzen's systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called Ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz' system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz' main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In a recent work, Ecumenical sequent calculi and a nested system were presented, and some very interesting proof theoretical properties of the systems were established. In this work we extend Prawitz' Ecumenical idea to alethic K-modalities