Arturo Tozzi

Center for Nonlinear Science, University of North Texas

1155 Union Circle, #311427

Denton, TX 76203-5017, USA, and

Computational Intelligence Laboratory, University of Manitoba, Winnipeg, Canada

Winnipeg R3T 5V6 Manitoba




James F. Peters

 Department of Electrical and Computer Engineering, University of Manitoba

75A Chancellor’s Circle, Winnipeg, MB R3T 5V6, Canada and

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey,

Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University

02040 Adıyaman, Turkey and Computational Intelligence Laboratory, University of

Manitoba, WPG, MB, R3T 5V6, Canada







When facing a proposition, e.g., a spoken or written phrase, the brain straightforwardly understands its grammar and discriminates whether it is true or false.  Unlike computers, the brain is indeed able to identify signs of sequences in terms of both syntactic symbols and semantic meaning.  However, the brain mechanisms of language processing are unidentified, and such a limited knowledge is also the cause of a long-standing problem in artificial intelligence and computational neuroscience: the unfeasibility for our syntaxic-, Boolean logic-based computers to cope with semantic expressions.   Here we show, based on the current literature, that an easy and testable algebraic topological approach gives helpful  insights into brain’s computational activity during semantic recognition.  Indeed, recent suggestions allow us to hypothesize that the semantic properties of a proposition are processed in brain dimensions higher than the syntactic ones.  Furthermore, we show how, in a fully reversible process, the syntactic elements embedded in Broca’s area might project to scattered semantic cortical zones, where the presence of higher functional dimensions gives rise to an increase in proposition’s information content.    Taking into account the dictates of novel versions of the Borsuk-Ulam and the fixed-point theorems, we build a  framework that provides a feasible explanation for semantics processing in the brain, and paves also the way to novel computers which nodes are built in higher dimensions.