Adding similarity-based reasoning capabilities to a Horn fragment of possibilistic logic with fuzzy constants

PLFC is a first-order possibilistic logic dealing with fuzzy constants and fuzzily restricted quantifiers. The refutation proof method in PLFC is mainly based on a generalized resolution rule which allows an implicit graded unification among fuzzy constants. However, unification for precise object constants is classical. In order to use PLFC for similarity-based reasoning, in this paper we extend a Horn-rule sublogic of PLFC with similarity-based unification of object constants. The Horn-rule sublogic of PLFC we consider deals only with disjunctive fuzzy constants and it is equipped with a simple and efficient version of PLFC proof method. At the semantic level, it is extended by equipping each sort with a fuzzy similarity relation, and at the syntactic level, by fuzzily “enlarging” each non-fuzzy object constant in the antecedent of a Horn-rule by means of a fuzzy similarity relation.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Molecular phylogenetics and temporal diversification in the genus Aeromonas based on the sequences of five housekeeping genes

Several approaches have been developed to estimate both the relative and absolute rates of speciation and extinction within clades based on molecular phylogenetic reconstructions of evolutionary relationships, according to an underlying model of diversification. However, the macroevolutionary models established for eukaryotes have scarcely been used with prokaryotes. We have investigated the rate and pattern of cladogenesis in the genus Aeromonas (γ-Proteobacteria, Proteobacteria, Bacteria) using the sequences of five housekeeping genes and an uncorrelated relaxed-clock approach. To our knowledge, until now this analysis has never been applied to all the species described in a bacterial genus and thus opens up the possibility of establishing models of speciation from sequence data commonly used in phylogenetic studies of prokaryotes. Our results suggest that the genus Aeromonas began to diverge between 248 and 266 million years ago, exhibiting a constant divergence rate through the Phanerozoic, which could be described as a pure birth process.

Atypical language organization in temporal lobe epilepsy revealed by a passive semantic paradigm

Background Mesial temporal lobe epilepsy (MTLE) is the most common type of focal epilepsy in adults and can be successfully cured by surgery. One of the main complications of this surgery however is a decline in language abilities. The magnitude of this decline is related to the degree of language lateralization to the left hemisphere. Most fMRI paradigms used to determine language dominance in epileptic populations have used active language tasks. Sometimes, these paradigms are too complex and may result in patient underperformance. Only a few studies have used purely passive tasks, such as listening to standard speech. Methods In the present study we characterized language lateralization in patients with MTLE using a rapid and passive semantic language task. We used functional magnetic resonance imaging (fMRI) to study 23 patients [12 with Left (LMTLE), 11 with Right mesial temporal lobe epilepsy (RMTLE)] and 19 healthy right-handed controls using a 6 minute long semantic task in which subjects passively listened to groups of sentences (SEN) and pseudo sentences (PSEN). A lateralization index (LI) was computed using a priori regions of interest of the temporal lobe. Results The LI for the significant contrasts produced activations for all participants in both temporal lobes. 81.8% of RMTLE patients and 79% of healthy individuals had a bilateral language representation for this particular task. However, 50% of LMTLE patients presented an atypical right hemispheric dominance in the LI. More importantly, the degree of right lateralization in LMTLE patients was correlated with the age of epilepsy onset. Conclusions The simple, rapid, non-collaboration dependent, passive task described in this study, produces a robust activation in the temporal lobe in both patients and controls and is capable of illustrating a pattern of atypical language organization for LMTLE patients. Furthermore, we observed that the atypical right-lateralization patterns in LMTLE patients was associated to earlier age at epilepsy onset. These results are in line with the idea that early onset of epileptic activity is associated to larger neuroplastic changes.