Proof-search and countermodel generation for non-normal modal logics: The theorem prover PRONOM

2021 ◽  
Vol 14 (2) ◽  
pp. 215-229
Author(s):  
Tiziano Dalmonte ◽  
Sara Negri ◽  
Nicola Olivetti ◽  
Gian Luca Pozzato
Keyword(s):  
Modal Logics ◽  
Experimental Results ◽  
Theorem Prover ◽  
Basic System ◽  
Sequent Calculi ◽  
Modal Formula ◽  
Left Hand ◽  
Proof Search ◽  
The Right ◽  
Normal Modal Logics

In this work we present PRONOM, a theorem prover and countermodel generator for non-normal modal logics. PRONOM implements some labelled sequent calculi recently introduced for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. PRONOM is inspired by the methodology of leanTAP and is implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof (a closed tree) in the labelled calculi having a sequent with an empty left-hand side and containing only that formula on the right-hand side as a root, otherwise PRONOM is able to extract a model falsifying it from an open, saturated branch. The paper shows some experimental results, witnessing that the performances of PRONOM are promising.

scholarly journals Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

2017 ◽  
Vol 46 (3/4) ◽  
Author(s):  
Krystyna Mruczek-Nasieniewska ◽  
Marek Nasieniewski
Keyword(s):  
Intuitionistic Logic ◽  
Deontic Logic ◽  
Modus Ponens ◽  
Modal Logics ◽  
Point Of View ◽  
Modal Operator ◽  
Modal Interpretation ◽  
Semantical Point ◽  
The Right ◽  
Normal Modal Logics

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9]). In (Došen; [2]) a logic N has been investigated in the language with negation; implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation (see [3; p. 300]). In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21 (see [4] and [13]). The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+.

scholarly journals Proof theory for quantified monotone modal logics

2019 ◽  
Vol 27 (4) ◽  
pp. 478-506
Author(s):  
Sara Negri ◽  
Eugenio Orlandelli
Keyword(s):  
Proof Theory ◽  
Modal Logics ◽  
Cut Elimination ◽  
Sequent Calculi ◽  
Completeness Proof ◽  
First Order ◽  
Constant Domains ◽  
Normal Modal Logics ◽  
Order Extension

Abstract This paper provides a proof-theoretic study of quantified non-normal modal logics (NNML). It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced is sound and complete with respect to the appropriate class of neighbourhood frames. In particular, the completeness proof constructs a formal derivation for derivable sequents and a countermodel for non-derivable ones, and gives a semantic proof of the admissibility of cut.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Is the Future the Right Time?

2010 ◽  
Vol 57 (4) ◽  
pp. 308-314 ◽  
Author(s):  
Marc Ouellet ◽  
Julio Santiago ◽  
Ziv Israeli ◽  
Shai Gabay
Keyword(s):  
Auditory Task ◽  
English Speakers ◽  
Visual Modality ◽  
Opposite Pattern ◽  
Time Line ◽  
Temporal Reference ◽  
Left Hand ◽  
Reading Direction ◽  
Mental Time Line ◽  
The Right

Spanish and English speakers tend to conceptualize time as running from left to right along a mental line. Previous research suggests that this representational strategy arises from the participants’ exposure to a left-to-right writing system. However, direct evidence supporting this assertion suffers from several limitations and relies only on the visual modality. This study subjected to a direct test the reading hypothesis using an auditory task. Participants from two groups (Spanish and Hebrew) differing in the directionality of their orthographic system had to discriminate temporal reference (past or future) of verbs and adverbs (referring to either past or future) auditorily presented to either the left or right ear by pressing a left or a right key. Spanish participants were faster responding to past words with the left hand and to future words with the right hand, whereas Hebrew participants showed the opposite pattern. Our results demonstrate that the left-right mapping of time is not restricted to the visual modality and that the direction of reading accounts for the preferred directionality of the mental time line. These results are discussed in the context of a possible mechanism underlying the effects of reading direction on highly abstract conceptual representations.

scholarly journals Hand Preference and Performance in Basketball Tasks

2019 ◽  
Vol 16 (22) ◽  
pp. 4336 ◽  
Author(s):  
Emanuela Gualdi-Russo ◽  
Natascia Rinaldo ◽  
Alba Pasini ◽  
Luciana Zaccagni
Keyword(s):  
Professional Training ◽  
Factor Model ◽  
Hand Preference ◽  
Control Group ◽  
Basketball Players ◽  
Confirmatory Factor Analyses ◽  
Left Hand ◽  
Confirmatory Factor ◽  
And Performance ◽  
The Right

The aims of this study were to develop and validate an instrument to quantitatively assess the handedness of basketballers in basketball tasks (Basketball Handedness Inventory, BaHI) and to compare it with their handedness in daily activities by the Edinburgh Handedness Inventory (EHI). The participants were 111 basketballers and 40 controls. All subjects completed the EHI and only basketballers filled in the BaHI. To validate the BaHI, a voluntary subsample of basketballers repeated the BaHI. Exploratory and confirmatory factor analyses supported a two-factor model. Our results show that: (i) Handedness score (R) in daily actions did not differ between basketball players (R by EHI = 69.3 ± 44.6) and the control group (R by EHI = 64.5 ± 58.6); (ii) basketballers more frequently favored performing certain sport tasks with the left hand or mixed hands (as highlighted by R by BaHI = 50.1 ± 47.1), although their choice was primarily the right hand in everyday gestures; and (iii) this preference was especially true for athletes at the highest levels of performance (R by BaHI of A1 league = 38.6 ± 58.3) and for those playing in selected roles (point guard’s R = 29.4 ± 67.4). Our findings suggest that professional training induces handedness changes in basketball tasks. The BaHI provides a valid and reliable measure of the skilled hand in basketball. This will allow coaches to assess mastery of the ball according to the hand used by the athlete in the different tasks and roles.

scholarly journals Digit Variability in Carotenoid Scores Obtained with the Veggie Meter: A Pilot Study (P02-001-19)

2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Velarie Ansu ◽  
Stephanie Dickinson ◽  
Alyce Fly
Keyword(s):  
Indiana University ◽  
Left Hand ◽  
Funding Sources ◽  
Right Hand ◽  
Period Data ◽  
The Mean ◽  
The Right ◽  
Post Hoc ◽  
Main Effects ◽  
Mean Square Errors

Abstract Objectives To determine which digit and hand have the highest and lowest skin carotenoid scores, to compare inter-and-intra-hand variability of digits, and to determine if results are consistent with another subject. Methods Two subjects’ first(F1), second(F2), third(F3) and fifth(F5) digits on both hands were measured for skin carotenoids with a Veggie Meter, for 3 times on each of 18 days over a 37-day period. Data were subjected to ANOVA in a factorial treatment design to determine main effects for hand (2 levels), digits (4), and days (18) along with interactions. Differences between digits were determined by Tukey's post hoc test. Results There were significant hand x digit, hand x day, digit x day, and hand x digit x day interactions and significant simple main effects for hand, digit, and day (all P < 0.001). Mean square errors were 143.67 and 195.62 for subject A and B, respectively, which were smaller than mean squares for all main effects and interactions. The mean scores ± SD for F1, F2, F3, and F5 digits for the right vs left hands for subject A were F1:357.13 ± 45.97 vs 363.74 ± 46.94, F2:403.17 ± 44.77 vs. 353.20 ± 44.13, F3:406.76 ± 43.10 vs. 357.11 ± 45.13, and F5:374.95 ± 53.00 vs. 377.90 ± 47.38. For subject B, the mean scores ± SD for digits for the right vs left hands were F1:294.72 ± 61.63 vs 280.71 ± 52.48, F2:285.85 ± 66.92 vs 252.67 ± 67.56, F3:268.56 ± 57.03 vs 283.22 ± 45.87, and F5:288.18 ± 34.46 vs 307.54 ± 40.04. The digits on the right hand of both subjects had higher carotenoid scores than those on the left hands, even though subjects had different dominant hands. Subject A had higher skin carotenoid scores on the F3 and F2 digits for the right hand and F5 on the left hand. Subject B had higher skin carotenoid scores on F5 (right) and F1 (left) digits. Conclusions The variability due to hand, digit, and day were all greater than that of the 3 replicates within the digit-day for both volunteers. This indicates that data were not completely random across the readings when remeasuring the same finger. Different fingers displayed higher carotenoid scores for each volunteer. There is a need to conduct a larger study with more subjects and a range of skin tones to determine whether the reliability of measurements among digits of both hands is similar across the population. Funding Sources Indiana University.

scholarly journals Sea Surface Salinity Response to Tropical Cyclones Based on Satellite Observations

2021 ◽  
Vol 13 (3) ◽  
pp. 420
Author(s):  
Jingru Sun ◽  
Gabriel Vecchi ◽  
Brian Soden
Keyword(s):  
Tropical Cyclones ◽  
Sea Surface ◽  
Sea Surface Salinity ◽  
Surface Salinity ◽  
Translation Speed ◽  
Salinity Stratification ◽  
Left Hand ◽  
In Situ Data ◽  
Salinity Response ◽  
The Right

Multi-year records of satellite remote sensing of sea surface salinity (SSS) provide an opportunity to investigate the climatological characteristics of the SSS response to tropical cyclones (TCs). In this study, the influence of TC winds, rainfall and preexisting ocean stratification on SSS evolution is examined with multiple satellite-based and in-situ data. Global storm-centered composites indicate that TCs act to initially freshen the ocean surface (due to precipitation), and subsequently salinify the surface, largely through vertical ocean processes (mixing and upwelling), although regional hydrography can lead to local departure from this behavior. On average, on the day a TC passes, a strong SSS decrease is observed. The fresh anomaly is subsequently replaced by a net surface salinification, which persists for weeks. This salinification is larger on the right (left)-hand side of the storm motion in the Northern (Southern) Hemisphere, consistent with the location of stronger turbulent mixing. The influence of TC intensity and translation speed on the ocean response is also examined. Despite having greater precipitation, stronger TCs tend to produce longer-lasting, stronger and deeper salinification especially on the right-hand side of the storm motion. Faster moving TCs are found to have slightly weaker freshening with larger area coverage during the passage, but comparable salinification after the passage. The ocean haline response in four basins with different climatological salinity stratification reveals a significant impact of vertical stratification on the salinity response during and after the passage of TCs.

scholarly journals Anatomical work-up of an individual with multiple muscular variants on both forearms

2021 ◽  
Author(s):  
Peter S. Hagedorn ◽  
Bernhard Hirt ◽  
Thomas Shiozawa ◽  
Peter H. Neckel
Keyword(s):  
Carpal Tunnel ◽  
Proximal Phalanx ◽  
Neurovascular Compression ◽  
Male Body ◽  
Muscle Belly ◽  
Left Hand ◽  
Palmaris Longus ◽  
Palmar Aponeurosis ◽  
The Right ◽  
Work Up

AbstractMuscular variants of the forearm are common and frequently cause neurovascular compression syndromes, especially when interfering with the compact topography of the carpal tunnel or the Canalis ulnaris. Here, we report on a male body donor with multiple muscular normal variations on both forearms. The two main findings are (1) an accessory variant muscle (AVM) on the right forearm originating from the M. brachioradialis, the distal radius, and the M. flexor pollicis longus. It spanned the wrist beneath the Fascia antebrachia and inserted at the proximal phalanx of the digitus minimus. (2) Moreover, we found a three-headed palmaris longus variant on the left arm with proximal origin tendon and a distal, trifurcated muscle belly, with separated insertions at the palmar aponeurosis, the flexor retinaculum, and, in analogy to the accessory muscle on the contralateral arm, at the base of the proximal phalanx of the digitus minimus. We found a considerable thickening of the left-hand median nerve right before entering the carpal tunnel indicative of a possible chronic compression syndrome adding clinical relevance to this anatomical case. We also discuss the notion that both, the AVM and the contralateral three-headed palmaris variant are developmental descendants of the M. palmaris longus. Additionally, we found a previously not recorded variant of the M. palmaris brevis on the left hand.

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