Contradictory reasoning network:an EEG and FMRI study

Contradiction is a cornerstone of human rationality, essential for everyday life and communication. We investigated electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) in separate recording sessions during contradictory judgments, using a logical structure based on categorical propositions of the Aristotelian Square of Opposition (ASoO). The use of ASoO propositions, while controlling for potential linguistic or semantic confounds, enabled us to observe the spatial temporal unfolding of this contradictory reasoning. The processing started with the inversion of the logical operators corresponding to right middle frontal gyrus (rMFG-BA11) activation, followed by identification of contradictory statement associated with in the right inferior frontal gyrus (rIFG-BA47) activation. Right medial frontal gyrus (rMeFG, BA10) and anterior cingulate cortex (ACC, BA32) contributed to the later stages of process. We observed a correlation between the delayed latency of rBA11 response and the reaction time delay during inductive vs. deductive reasoning. This supports the notion that rBA11 is crucial for manipulating the logical operators. Slower processing time and stronger brain responses for inductive logic suggested that examples are easier to process than general principles and are more likely to simplify communication. © 2014 Porcaro et al

Universal vs. particular reasoning: a study with neuroimaging techniques

The article investigates some general properties of universal vs. particular propositions occuring in syllogistic arguments, in order to explore the kind of interaction played by these two forms of reasoning inside cognition. The theoretical framework of our analysis is represented by recent developments of linear logic, focusing on the distinction between positive vs. negative status of logical operators (connectives and quantifiers). In the first part of the article, this distinction is introduced and applied to the analysis of the categorical propositions occurring in Aristotelian syllogism, the deductive paradigm particularly considered in psychological studies about human reasoning. In the second part of the article, an experimental research is presented in which the positive vs. negative alternation is studied in the transition from a universal (vs. a particular) categorical proposition to its contradictory, a particular (vs. a universal) categorical proposition; the experimental research is based on a reasoning task which shows that significant differences are exhibited by the two types of transitions. © The Author 2013. Published by Oxford University Press. All rights reserved

Cyclic Multiplicative Proof Nets of Linear Logic with an Application to Language Parsing

This paper concerns a logical approach to natural language parsing based on proof nets (PNs), i.e. de-sequentialized proofs, of linear logic (LL). In particular, it presents a simple and intuitive syntax for PNs of the cyclic multiplicative fragment of linear logic (CyMLL). The proposed correctness criterion for CyMLL PNs can be considered as the non-commutative counterpart of the famous Danos-Regnier (DR) criterion for PNs of the pure multiplicative fragment (MLL) of LL. The main intuition relies on the fact that any DR-switching (i.e. any correction or test graph for a given PN) can be naturally viewed as a seaweed, i.e. a rootless planar tree inducing a cyclic order on the conclusions of the given PN. Dislike the most part of current syntaxes for non-commutative PNs, our syntax allows a sequentialization for the full class of CyMLL PNs, without requiring these latter must be cut-free. Moreover, we give a simple characterization of CyMLL PNs for Lambek Calculus and thus a geometrical (non inductive) way to parse phrases or sentences by means of Lambek PNs

Cyclic multiplicative-additive proof nets of linear logic with an application to language parsing

This paper concerns a logical approach to natural language parsing based on proof nets (PNs), i.e. de-sequentialized proofs, of linear logic (LL). In particular, it presents a syntax for PNs of the cyclic multiplicative and additive fragment of linear logic (CyMALL). Any proof structure (PS), in Girards style, is weighted by boolean monomial weights, moreover, its conclusions Γ (a sequence of formulas occurrences) are endowed with a cyclic order σ, i.e., σ(Γ). Naively, a CyMALL PS π with conclusions σ(Γ) is correct if, for any slice ϕ(π) (obtained by a boolean valuation ϕ of π) there exists an additive resolution (i.e. a multiplicative refinement of ϕ(π)) that is a CyMLL PN with conclusions σ(Γr), where Γr is an additive resolution of Γ (i.e. a choice of an additive subformula for each formula of Γ). In its turn, the correctness criterion for CyMLL PNs can be considered as the non-commutative counterpart of the famous Danos-Regnier (DR) criterion for PNs of the pure multiplicative fragment (MLL) of LL. The main intuition relies on the fact that any DR-switching (i.e. any correction or test graph for a given PN) can be naturally viewed as a seaweed, i.e. a rootless planar tree inducing a cyclic order on the conclusions of the given PN. Dislike the most part of current syntaxes for non-commutative PNs our syntax allows a sequentialization for the full class of CyMLL PNs, without requiring these latter must be cut-free. Moreover, we give a characterization of CyMALL PNs for the extended (MALL) Lambek Calculus and thus a geometrical (non inductive) way to parse phrases or sentences. In particular additive Lambek PNs allow to parse phrases containing words with syntactical ambiguity (i.e. words with polymorphic type)