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![The morphology of miracidia. A. the general morphology of Trichobilharzia szidati (from [23]); B. the general morphology of Trichobilharzia regenti (left) and the arrangement of ciliated plates (right), scale bar = 25mm (from [16])](profile/Andrew-Schumann/publication/276511992/figure/fig3/AS:329468343275522@1455562782157/The-morphology-of-miracidia-A-the-general-morphology-of-Trichobilharzia-szidati-from.png)
The morphology of miracidia. A. the general morphology of Trichobilharzia szidati (from [23]); B. the general morphology of Trichobilharzia regenti (left) and the arrangement of ciliated plates (right), scale bar = 25mm (from [16])
Source publication
In the paper, a new syllogistic system is built up. This system simulates a massive-parallel behavior in the propagation of collectives of parasites. In particular, this system simulates the behavior of collectives of trematode larvae (miracidia and cercariae).
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Citations
... Thompson (1982) extended the Aristotelian system by adding "many, more, and most" , staying faithful to the principles of the original system, and introduced five-quantifier square of opposition. Briefly, syllogistic theories have been taking place in many applications of wide areas, particularly generalized quantifiers of natural language theory (Moss 2016;van Eijck 1985van Eijck , 2015van Eijck , 2005van Rooij 2010;D'Alfonso 2012;van Benthem 1985), algebraic structures (Sotirov 1999;Bocharov 1986;Peirce 1880;Black 1945), formal logic (Moss 2008(Moss , 2010a(Moss , b, 2011Pratt-Hartmann and Moss 2009), unconventional systems (Schumann and Adamatzky 2015;Schumann 2013;Schumann and Akimova 2015), and some applications on infinite sets Moss and Topal (2018). Endrullis and Moss (2015) introduced a syllogistic logic containing the quantifier most on finite sets. ...
This paper proposes a formalization of the class of sentences quantified by
\textit{most}, which is also interpreted as {\em proportion of} or {\em majority of}
depending on the domain of discourse. We consider sentences of the form
``\textit{Most A are B}", where \textit{A} and \textit{B} are plural nouns and the
interpretations of $ A $ and $ B $ are infinite subsets of $ \mathbb{N} $. There are two
widely used semantics for \textit{Most A are B}: (i) $C(A \cap B) > C(A\setminus B) $
and (ii) $ C(A\cap B) > \dfrac{C(A)}{2} $, where $ C(X) $ denotes the cardinality of a
given finite set $ X $. Although (i) is more descriptive than (ii), it also produces a
considerable amount of insensitivity for certain sets. Since the quantifier {\em most}
has a solid cardinal behaviour under the interpretation {\em majority} and has a slightly
more statistical behaviour under the interpretation {\em proportional of}, we consider an
alternative approach in deciding quantity-related statements regarding infinite sets. For
this we introduce a new semantics using {\em natural density} for sentences in which
interpretations of their nouns are infinite subsets of $ \mathbb{N} $, along with a list of
the axiomatization of the concept of natural density. In other words, we take the
standard definition of the semantics of \textit{most} but define it as applying to finite
approximations of infinite sets computed to the limit.
... Thompson [9] extended the Aristotelian system by adding "many, more, and most" , staying faithful to the principles of the original system, and introduced five-quantifier square of opposition. Briefly, syllogistic theories have been taking place in many applications of wide areas, particularly generalized quantifiers of natural language theory [10,12,13,14,15,17,18], algebraic structures [19,20,21,22], formal logic [23,24,25,26,27], unconventional systems [28,29,30], and some applications on infinite sets [31]. ...
This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form "Most A are B ", where A and B are plural nouns and the interpretations of A and B are infinite subsets of N. There are two widely used semantics for Most A are B : (i) C(A ∩ B) > C(A \ B) and (ii) C(A ∩ B) > C(A) 2 , where C(X) denotes the cardinality of a given finite set X. Although (i) is more descriptive than (ii), it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantity-related statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of N, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit.
... Thompson extended the ancient system with "Many, More, and Most " faithful to the original and gave five-quantifier square of opposition [9]. Briefly, syllogistic theories have been taking place in wide applications of different areas such as in natural language theory and generalized quantifiers [10,12,13,14,15,17,18], in algebraic structures [19,20,21,22], in formal logic [23,24,25,26,27], in unconventional systems [28,29,30], and on infinite sets [31]. ...
This paper considers the quantified simple sentences by \textit{Most}, sometimes referred to as proportional, sometimes the majority. The sentence form: \textit{Most A are B} where \textit{A} and \textit{B} are plural nouns. $ A $ and $ B $ range over elements of $ P(\mathbb{N}) $. Moreover, $ A $ and $ B $ may appear complemented (i.e., as $ Non-A $ and $ Non-B $). Two different but equivalent semantics are for \textit{Most A are B} as (i) $ C(A \cap B) > C(A\setminus B) $ and (ii) $ C(A\cap B) > \dfrac{C(A)}{2} $ where $ C(X) $ is the cardinality of the set $ X $. Both semantics work well on finite sets but exhibit problematic behaviors on infinite sets since division is undefined on cardinal arithmetic. Although semantics (i) is more descriptive than semantics (ii), it also produces insensitivity for certain sets. \textquotedblleft Most" has a solid cardinal structure under the interpretation of the majority, and has the more statistical structure with proportional interpretation, and this statistical interpretation provides more flexible range of motion. For all these reasons, we introduce a new semantics with natural density for the sentences ranging over $ \mathbb{N} $. We also give an axiomatization of this logic.
... The theory of non-linear permutation groups can be used for designing reversible logic gates on any behavioural systems [9]. The simple versions of these gates are represented by logic circuits constructed on the basis of the performative syllogistic [17,[28][29][30]. It seems to be natural for behavioural systems and these circuits have a very high accuracy in implementing. ...
... Unfortunately, the computational power of their implementations on swarms is too low [26]. To make computations on trees more expressive I have proposed the performative syllogistic-a syllogistic system of propagation [17,[28][29][30]. This system can logically simulate a massive-parallel behaviour in the propagation of collectives of Trematode larvae (miracidia and cercariae) and other swarms. ...
In accordance with behaviourism, any animal behaviour based on unconditioned and conditioning reflexes can be controlled or even managed by stimuli in the environment: attractants (motivational reinforcement) and repellents (motivational punishment). In the meanwhile, there are the following two main stages in reactions to stimuli: sensing (perceiving signals) and motoring (appropriate direct reactions to signals). In this book, the strict limits of behaviourism have been studied from the point of view of symbolic logic and algebraic mathematics: How far can animal behaviours be controlled by the topology of stimuli? In other words, how far can we design unconventional computers on the basis of animal reactions to stimuli?
... For these concepts, therefore, we can not define an including relation and we need a novel formal system. Some applications of that new syllogistic are proposed in Schumann and Akimova (2015). ...
The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called \( \mathcal {R}(\forall ,\exists ) \) and \( \mathcal {G}(\forall ,\exists ) \) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics (without Boolean connectives) are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics (bounded meet semi-lattice) of the logics using congruence theory.
... Generally, the logic of propagation of groups of alcoholics has the same axioms as the logic of parasite propagation for Schistosomatidae sp. (Schumann, Akimova, 2015) as well as the same axioms as the logic of slime mould expansion (Schumann, 2015(Schumann, , 2016. The difference is that instead of syllogistics for Schistosomatidae sp. ...
... The difference is that instead of syllogistics for Schistosomatidae sp. (Schumann, Akimova, 2015) and for slime mould (Schumann, 2016), where preference relations are simple and express only attractions by food, we involve many performative actions (verbs), which express a desire to drink together, within modal logics Ki and K'i. The logic Ki is used to formalize lateral inhibition in distributing people to drink jointly and the logic K'i is used to formalize lateral activation in distributing people to drink jointly. ...
... For fixing Physarum computing on nutrient-rich substrate, we have constructed a non-Aristotelian syllogistic (performative syllogistic) [9], [10], [15], [19], [36] that models Physarum simultaneous propagations in all directions (i.e. it is massive-parallel). This system can logically simulate a massive-parallel behaviour in the propagation of any swarm. ...
... This system can logically simulate a massive-parallel behaviour in the propagation of any swarm. In particular, this system simulates the behaviour of collectives of Trematode larvae (miracidia and cercariae) [36]. Also, this syllogistic system of propagation can be used as basic logical theory for quantum logic (without logical atoms) [21]. ...
... Notice that the Aristotelian syllogistic is implementable for Physarum computing on nutrient-poor substrate, while performative syllogistic is applicable for Physarum computing on nutrient-rich substrate [9], [10], [15], [19], [36]. Performative syllogistic is an extension of Aristotelian one and includes the latter as its own part. ...
The paper considers main features of two groups of logics for biological devices, called Physarum Chips, based on the plasmodium. Let us recall that the plasmodium is a single cell with many diploid nuclei. It propagates networks by growing pseudopodia to connect scattered nutrients (pieces of food). As a result, we deal with a kind of computing. The first group of logics for Physarum Chips formalizes the plasmodium behaviour under conditions of nutrient-poor substrate. This group can be defined as standard storage modification machines. The second group of logics for Physarum Chips covers the plasmodium computing under conditions of nutrient-rich substrate. In this case the plasmodium behaves in a massively parallel manner and propagates in all possible directions. The logics of the second group are unconventional and deal with non-well-founded data such as infinite streams.
... The formal properties of this axiomatic system are considered in [17]. [18]. ...
... Within this system we can study how the plasmodium realizes LA at the motor stage in occupying all possible attractants in any direction if it can perserve them. A model M = M , | · | x for this syllogistic, where M is the set of attractants and |X| x ⊆ M is a meaning of syllogistic letter X which is understood as all attractants reachable for the plasmodium from the point x, is defined as follows [18]: M |= 'alternative y is at least as good as alternative x' iff |X| x = ∅, |X| y = ∅, and |X| x ∩ |X| y = ∅, i.e., the plasmodium can move from neighbors of y to x and it can move from neighbors of x to y; M |= 'alternative y is not at least as bad as alternative x' iff y / ∈ |X| x and x / ∈ |X| y , i.e., the plasmodium cannot move from neighbors of y to x and it cannot move from neighbors of x to y; M |= 'alternative y is at least as bad as alternative x' iff y ∈ |X| x or x ∈ |X| y , i.e., the plasmodium can move from neighbors of y to x or it can move from neighbors of x to y; M |= 'alternative y is not at least as good as alternative x' iff y / ∈ |X| x or x / ∈ |X| y , i.e., the plasmodium cannot move from neighbors of y to x or it cannot move from neighbors of x to y; M |= p ∧ q iff M |= p and M |= q; ...
This paper examines two main possibilities of pairwise comparisons analysis: first, pairwise comparisons within a lattice, in this case these comparisons can be measurable by numbers; second, comparisons beyond any lattice, in this case these comparisons cannot be measurable in principle. We show that the first approach to pairwise comparisons analysis is based on the conventional square of opposition and its generalization, but the second approach is based on unconventional squares of opposition. Furthermore, the first approach corresponds to lateral inhibition in transmission signals and the second approach corresponds to lateral activation in transmission signals.
I distinguish the swarm behaviour from the social one. The swarm behaviour is carried out without symbolic interactions, but it is complex, as well. In this paper, I show that an addictive behaviour of humans can be considered a kind of swarm behaviour, also. The risk of predation is a main reason of reducing symbolic interactions in human group behaviours, but there are possible other reasons like addiction. An addiction increases roles of addictive stimuli (e.g. alcohol, morphine, cocaine, sexual intercourse, gambling, etc.) by their reinforcing and intrinsically rewarding and we start to deal with a swarm. I show that the lateral inhibition and lateral activation are two fundamental patterns in sensing and motoring of swarms. The point is that both patterns allow swarms to occupy several attractants and to avoid several repellents at once. The swarm behaviour of alcoholics follows the lateral inhibition and lateral activation, too. In order to formalize this intelligence, I appeal to modal logics K and its modification K’. The logic K is used to formalize preference relation in the case of lateral inhibition in distributing people to drink jointly and the logic K’ is used to formalize preference relation in the case of lateral activation in distributing people to drink jointly.
In the p-adic valued universe of stimuli for controlling the swarm behaviour (including swarm sensing and motoring), we can define syllogistic propositions with two quantifiers: ‘all neighbours of an attractant/repellent’ and ‘some neighbours of an attractant/repellent’. In this chapter, I examine Aristotelian and non-Aristotelian syllogistics for simulating the swarms. In the Aristotelian syllogistic the models verifying swarming are well-founded and in the non-Aristotelian syllogistic the models verifying swarming are non-well-founded (i.e. they have no logical atoms).
