Rafael H. Bordini, John A. Campbell and Renata Vieira (1998)
Journal of Artificial Societies and Social Simulation vol. 1, no. 4, <http://jasss.soc.surrey.ac.uk/1/4/3.html>
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Received: 21-Aug-98 Accepted: 10-Oct-98 Published: 15-Oct-98
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Definition 1 (Acceptance Relation). Acceptance is an empirical relation between users and sentences of a language, observed by an experimenter who asks questions by means of a set of sentences forming a logical theory. Whenever an agent answers affirmatively to (has a positive attitude towards) one of these sentences we say that the agent accepts that sentence (which must belong to the set of sentences given by the experimenter) at that time.
Definition 2 (Subjective Quasi-Intension).   The notion of subjective quasi-intension for an individual constant (term) is defined as the properties associated with the term as expressed in the sentences which a given language user accepts at a certain time.
Definition 3 (Intersubjective Quasi-Intension).   This concept regards groups of language users, rather than individuals, at a certain time. An intersubjective quasi-intension is the equivalence class of all the subjective quasi-intensions of a certain group of users of the language.
Definition 4 (Intensional Ontology of Terms).   An Intensional Ontology of Terms (IOT) is a set of terms where each one is associated with the minimal set of predicates (properties) that is necessary and sufficient to distinguish (unequivocally) itself from every other term in the universe of discourse of a communicating society of agents.
Object A is named: something to eat, sandwich, ham sandwich.
Object B is named: something to eat, pie, apple pie.
Object C is named: something to eat, pie, cherry pie.
Object D is named: something to eat, ice-cream.
and the following abbreviation for the type Sent:
where TimeInstant is taken to be the set of constants representing time instants as it is intuitively understood. Term is the set of terms (also called individual constants) of the Communication Language (CL) used by the agents in any target society. Pred is the set of predicative constants (predicates) from CL. A sentence (Sent) of CL is a pair containing a predicate and a term, meaning that the term has the property (attribute) indicated by the predicate. We consider here only sentences of this sort; the consistent acceptance of sentences including the logical connectives by communicating agents within the quasi-intensional approach is given in Vieira and da Rocha Costa (1993).
where CSoc is a TSocId referring to the cricket society; we say that the cricket society has two informant agents identified by IAg1 and IAg2 (only two for the sake of simplicity); and we have used the following acronyms: Human Being (HB), Throws the Ball (TB), Throws the Ball Fast (TBF), Throws the Ball Slowly (TBS), Is Strong (IS), Is Accurate (IA), Carries a Bat (CB), Wears Gloves (WG), location Where the game is Played (WP), Field Partition (FP), to the Left of a Right-handed Batsman (LRB), to the Right of a Right-handed Batsman (RRB) and Centre of the Field (CF). We have also used fastblr for fast-bowler, slowblr for slow-bowler and wicketkpr for wicketkeeper.
we get the following IOT:
which would be passed on to find_taxonomical_relation. This in turn would call find_segregate(hbiot) which would return a pair, its first coordinate being segregate(player,HB), because HB is the predicate that all terms have in common. The second coordinate returned by find_segregate would be rhbiot, the remaining terms from hbiot:
2 We do not formalise the idea of groups of agents (and therefore the concept of Societal quasi-intension cannot be formalised either) in this paper, but the extension should not impose any difficulties.
3 In this particular context, the representational terms are those used in the communication language of a MAS.
4 An example in the context of the game of cricket, which is used as a case study in Section 5, is the predicate "is a cricket player" in hypernymy relation to "is a batsman", as batsman is a type of player.
5 Note that Frake uses the word object meaning anything regarded as a member of a category, whether perceptible or not.
6 We shall use that technical term below, even though it does not sound natural in ordinary English as a noun.
7 The example given in Frake (1969) concerns a conversation at a lunch counter, and has been abridged here.
8 It seems to us that, as the ethnographer is interested in testing terminological contrast, asking a question with the expectation of a negative reply has the following rationale. Forming a question with a wrong segregate, but one that is at the one particular level of inclusion (i.e., the vertical dimension of generalisation) where contrast is to be tested, will direct the answer from the informant--in its complementary part, that is, after "No"--to state the appropriate segregate at that particular level of inclusion, thus giving evidence of the contrasting relation between the inquired-about segregate and the one that occurs in the reply.
9 Note that Term (and Pred, mentioned next) are infinite domains; particular target societies will specify the subset of terms (and predicates) they use, as we shall see later.
10 Given the actual infrastructure of network services, this is not an unrealistic supposition.
11 Note that in the present formalisation we do not constrain the ontological description of a term to have a minimal set of properties as suggested in Definition 4. See further discussion about this in Section 6.
12 Note that a -expression is not allowed here because several predicates yielding the same segregate size may exist. We therefore state only that sp belongs to the set of predicates yielding the same largest segregate size (which is a somewhat ambiguous, but suitable for the purpose here).
13 The simplifications concern mainly some of the global definitions for the basic setting (e.g. access to TSs), which are not directly implementable in the Z tools used. All main algorithms are shown to work as intended in the animated version.
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Elements of the Z Notation
In Z, schemas are used to describe both static and dynamic aspects of a system. The static aspects include:
the states it can occupy;
the invariant relationships that are maintained as the systems moves from state to state.
The dynamic aspects include:
the operations that are possible;
the relationships between their inputs and outputs;
the changes of state that happen.
We next introduce in a concise way the subset of the Z notation that we have used in this paper. The Figure is borrowed, with their kind permission, from d'Inverno and Luck (1998), but adapted to the particular subset of the Z notation that has been used in this paper. Also, we have improved and restructured their figure, based partially on (Jia 1995) and (Spivey 1992).
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