TY - JOUR
TI - Quantum effect logic in cognition
AU - Jacobs, Bart
T2 - Journal of Mathematical Psychology
AB - This paper illustrates applications of a new, modern version of quantum logic in quantum cognition. The new logic uses ‘effects’ as predicates, instead of the more restricted interpretation of predicates as projections — which is used so far in this area. Effect logic involves states and predicates, validity and conditioning, and also state and predicate transformation via channels. The main aim of this paper is to demonstrate the usefulness of this effect logic in quantum cognition, via many high-level reformulations of standard examples. The usefulness of the logic is greatly increased by its implementation in the programming language Python.
DA - 2017/12/01/
PY - 2017
DO - 10/gcnkcj
DP - ScienceDirect
VL - 81
SP - 1
EP - 10
J2 - Journal of Mathematical Psychology
LA - en
SN - 0022-2496
UR - http://www.sciencedirect.com/science/article/pii/S0022249617300378
Y2 - 2019/11/22/22:19:41
KW - Categorical probability theory
KW - Effectus theory
KW - Psychology
ER -
TY - JOUR
TI - Using category theory to assess the relationship between consciousness and integrated information theory
AU - Tsuchiya, Naotsugu
AU - Taguchi, Shigeru
AU - Saigo, Hayato
T2 - Neuroscience Research
AB - One of the most mysterious phenomena in science is the nature of conscious experience. Due to its subjective nature, a reductionist approach is having a hard time in addressing some fundamental questions about consciousness. These questions are squarely and quantitatively tackled by a recently developed theoretical framework, called integrated information theory (IIT) of consciousness. In particular, IIT proposes that a maximally irreducible conceptual structure (MICS) is identical to conscious experience. However, there has been no principled way to assess the claimed identity. Here, we propose to apply a mathematical formalism, category theory, to assess the proposed identity and suggest that it is important to consider if there exists a proper translation between the domain of conscious experience and that of the MICS. If such translation exists, we postulate that questions in one domain can be answered in the other domain; very difficult questions in the domain of consciousness can be resolved in the domain of mathematics. We claim that it is possible to empirically test if such a functor exists, by using a combination of neuroscientific and computational approaches. Our general, principled and empirical framework allows us to assess the relationship between the domain of consciousness and the domain of mathematical structures, including those suggested by IIT.
DA - 2016/06/01/
PY - 2016
DO - 10/ggdf95
DP - ScienceDirect
VL - 107
SP - 1
EP - 7
J2 - Neuroscience Research
LA - en
SN - 0168-0102
UR - http://www.sciencedirect.com/science/article/pii/S0168010215002989
Y2 - 2019/11/22/20:54:32
KW - Psychology
KW - Sketchy
ER -
TY - JOUR
TI - Conciliating neuroscience and phenomenology via category theory
AU - Ehresmann, Andrée C.
AU - Gomez-Ramirez, Jaime
T2 - Progress in Biophysics and Molecular Biology
T3 - Integral Biomathics: Life Sciences, Mathematics, and Phenomenological Philosophy
AB - The paper discusses how neural and mental processes correlate for developing cognitive abilities like memory or spatial representation and allowing the emergence of higher cognitive processes up to embodied cognition, consciousness and creativity. It is done via the presentation of MENS (for Memory Evolutive Neural System), a mathematical methodology, based on category theory, which encompasses the neural and mental systems and analyzes their dynamics in the process of ‘becoming’. Using the categorical notion of a colimit, it describes the generation of mental objects through the iterative binding of distributed synchronous assemblies of neurons, and presents a new rationale of spatial representation in the hippocampus (Gómez-Ramirez and Sanz, 2011). An important result is that the degeneracy of the neural code (Edelman, 1989) is the property allowing for the formation of mental objects and cognitive processes of increasing complexity order, with multiple neuronal realizabilities; it is essential “to explain certain empirical phenomena like productivity and systematicity of thought and thinking (Aydede 2010)”. Rather than restricting the discourse to linguistics or philosophy of mind, the formal methods used in MENS lead to precise notions of Compositionality, Productivity and Systematicity, which overcome the dichotomic debate of classicism vs. connectionism and their multiple facets. It also allows developing the naturalized phenomenology approach asked for by Varela (1996) which “seeks articulations by mutual constraints between phenomena present in experience and the correlative field of phenomena established by the cognitive sciences”, while avoiding their pitfalls.
DA - 2015/12/01/
PY - 2015
DO - 10/f75jzr
DP - ScienceDirect
VL - 119
IS - 3
SP - 347
EP - 359
J2 - Progress in Biophysics and Molecular Biology
LA - en
SN - 0079-6107
UR - http://www.sciencedirect.com/science/article/pii/S0079610715001005
Y2 - 2019/11/28/23:48:27
KW - Biology
KW - Emergence
KW - Neuroscience
KW - Psychology
KW - Sketchy
ER -