2,883 research outputs found
On Sub-Propositional Fragments of Modal Logic
In this paper, we consider the well-known modal logics ,
, , and , and we study some of their
sub-propositional fragments, namely the classical Horn fragment, the Krom
fragment, the so-called core fragment, defined as the intersection of the Horn
and the Krom fragments, plus their sub-fragments obtained by limiting the use
of boxes and diamonds in clauses. We focus, first, on the relative expressive
power of such languages: we introduce a suitable measure of expressive power,
and we obtain a complex hierarchy that encompasses all fragments of the
considered logics. Then, after observing the low expressive power, in
particular, of the Horn fragments without diamonds, we study the computational
complexity of their satisfiability problem, proving that, in general, it
becomes polynomial
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
Generic Modal Cut Elimination Applied to Conditional Logics
We develop a general criterion for cut elimination in sequent calculi for
propositional modal logics, which rests on absorption of cut, contraction,
weakening and inversion by the purely modal part of the rule system. Our
criterion applies also to a wide variety of logics outside the realm of normal
modal logic. We give extensive example instantiations of our framework to
various conditional logics. For these, we obtain fully internalised calculi
which are substantially simpler than those known in the literature, along with
leaner proofs of cut elimination and complexity. In one case, conditional logic
with modus ponens and conditional excluded middle, cut elimination and
complexity were explicitly stated as open in the literature
More than one way to see it: Individual heuristics in avian visual computation
Comparative pattern learning experiments investigate how different species find regularities in sensory input, providing insights into cognitive processing in humans and other animals. Past research has focused either on one species’ ability to process pattern classes or different species’ performance in recognizing the same pattern, with little attention to individual and species-specific heuristics and decision strategies. We trained and tested two bird species, pigeons (Columba livia) and kea (Nestor notabilis, a parrot species), on visual patterns using touch-screen technology. Patterns were composed of several abstract elements and had varying degrees of structural complexity. We developed a model selection paradigm, based on regular expressions, that allowed us to reconstruct the specific decision strategies and cognitive heuristics adopted by a given individual in our task. Individual birds showed considerable differences in the number, type and heterogeneity of heuristic strategies adopted. Birds’ choices also exhibited consistent species-level differences. Kea adopted effective heuristic strategies, based on matching learned bigrams to stimulus edges. Individual pigeons, in contrast, adopted an idiosyncratic mix of strategies that included local transition probabilities and global string similarity. Although performance was above chance and quite high for kea, no individual of either species provided clear evidence of learning exactly the rule used to generate the training stimuli. Our results show that similar behavioral outcomes can be achieved using dramatically different strategies and highlight the dangers of combining multiple individuals in a group analysis. These findings, and our general approach, have implications for the design of future pattern learning experiments, and the interpretation of comparative cognition research more generally
Automated Synthesis of Tableau Calculi
This paper presents a method for synthesising sound and complete tableau
calculi. Given a specification of the formal semantics of a logic, the method
generates a set of tableau inference rules that can then be used to reason
within the logic. The method guarantees that the generated rules form a
calculus which is sound and constructively complete. If the logic can be shown
to admit finite filtration with respect to a well-defined first-order semantics
then adding a general blocking mechanism provides a terminating tableau
calculus. The process of generating tableau rules can be completely automated
and produces, together with the blocking mechanism, an automated procedure for
generating tableau decision procedures. For illustration we show the
workability of the approach for a description logic with transitive roles and
propositional intuitionistic logic.Comment: 32 page
A new approach for improving coronary plaque component analysis based on intravascular ultrasound images
Virtual histology intravascular ultrasound (VH-IVUS) is a clinically available technique for atherosclerosis plaque characterization. It, however, suffers from a poor longitudinal resolution due to electrocardiogram (ECG)-gated acquisition. This article presents an effective algorithm for IVUS image-based histology to overcome this limitation. After plaque area extraction within an input IVUS image, a textural analysis procedure consisting of feature extraction and classification steps is proposed. The pixels of the extracted plaque area excluding the shadow region were classified into one of the three plaque components of fibro-fatty (FF), calcification (CA) or necrotic core (NC) tissues. The average classification accuracy for pixel and region based validations is 75% and 87% respectively. Sensitivities (specificities) were 79% (85%) for CA, 81% (90%) for FF and 52% (82%) for NC. The kappa (kappa) = 0.61 and p value = 0.02 indicate good agreement of the proposed method with VH images. Finally, the enhancement in the longitudinal resolution was evaluated by reconstructing the IVUS images between the two sequential IVUS-VH images
A tableau-like proof procedure for normal modal logics
AbstractIn this paper a new proof procedure for some propositional and first-order normal modal logics is given. It combines a tableau-like approach and a resolution-like inference. Completeness and decidability for some propositional logics are proved. An extension for the first-order case is presented
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