Oneironomics | Algebraic Semiotics
When was the final time we had a brand new lead to semiotics? It’s a ceremony of passage within the humanities to put in writing papers stuffed with ‘signifiers’ and ‘signifieds’, and later to problematize this mannequin (Derrida, D&G), however the method is essentially set in stone. It’s a deep disgrace: if solely semiotics had superior on a par with linguistics, many fields resembling human-computer interplay might have progressed way more.
If anybody can treatment this, Joseph Goguen (1941-2006) is the man for the job. His remarkably prolific analysis consists of categorical fuzzy set concept, inventing the OBJ household of programming languages (e.g. CafeOBJ, Maude), and creating the speculation of ‘establishments’ as invariant properties of all logical programs. He was additionally a practising Buddhist, and editor-in-chief of the Journal of Consciousness Research.
All these come collectively in Goguen’s algebraic semiotics, which makes use of class concept to formalize the notion of sign-system, serving as a principled method to person interface design. The rabbit-hole goes fairly deep, and the primary concepts are strewn all through quite a few papers. This submit provides a self-contained introduction to algebraic semiotics, outlining semiotic morphisms as mappings between sign-systems, conceptual mixing as condensation of morphisms, hidden algebra as formalizing dynamic creation of which means, and polymorphic poetics as computational semiology.
Signal-Programs
The important thing perception of semiotics is that as an alternative of which means being inherent to an indication, indicators purchase which means differentially, by way of a system of oppositions. Naturally, we don’t wish to spell these out, which for n indicators implies n*(n-1)/2
oppositions. If we used units as a framework, we might be in for a tough time, not least as a result of our understandings are at all times solely partial — this wouldn’t go away room for indicators we don’t learn about, or might not wish to embrace (1999: 250).
As an alternative, an method utilizing algebra provides the construction we’d like whereas additionally permitting open programs. Goguen provides a proper definition of a sign-system that I’ll clarify intimately, so the reader might wish to simply skim till the following part. An indication-system is manufactured from the next elements (2004: 4):
- a signature that declares kinds, subsorts, and operations
- a subsignature of information kinds and knowledge capabilities
- a set of axioms (e.g. equations) that act as constraints
- a degree ordering on kinds, together with a maximal ordering referred to as ‘high’
- a precedence ordering on constructors on the identical degree
First, a ‘kind’ is the kind of an indication. It may be mundane, like separating textual content from numbers, however may also be elaborate, resembling elements of a multimedia show, with nested subsorts and supersorts. Types have a part-whole hierarchy (‘degree ordering’): for instance a menu bar and scroll bar could also be on the identical degree, however at a decrease degree than the window of which they’re components (Harrell, 2013: 133).
Operations embrace constructors that construct new indicators from previous indicators as components, and selectors that pull out components from compound indicators (2004: 4). Constructors can have parameters, such a picture of a cat that takes parameters for its shade, measurement, and placement (Goguen & Harrell, 2005a: 86); every parameter of a constructor has a corresponding selector to extract its worth (1999: 263). These extra normal attributes of indicators (e.g. colours, booleans, integers) are ‘knowledge kinds’, and go within the subsignature.
Axioms are logical formulation manufactured from constructors, capabilities and predicates, and constrain the set of doable indicators (Goguen & Harrell, 2005a: 86). For instance, we might wish to stipulate that every one home windows on a display screen are under a sure measurement, or that an integer has no main zeros (Harrell, 2013: 132).
The primary 4 gadgets make an algebraic concept, which simply means a declaration of symbols plus guidelines to limit their use (1999: 244). That is what makes Goguen’s semiotics ‘algebraic’. Typically he refers to a sign-system as a ‘semiotic concept’, versus a particular mannequin (i.e. interpretation) that instantiates it. The category of fashions that fulfill a given concept known as its semiotic area (2003: 2).
Be aware that we add some further construction by way of a precedence ordering, which is assigned to constructors and their arguments to specific the relative significance of the indicators they construct (2003: 2). Therefore, “priorities point out the relative significance of subsigns at a given degree” (2004: 4). The extent and precedence ordering are the primary ways in which social context is built-in right into a mannequin.
In sum: “Types classify indicators, operations assemble indicators, knowledge kinds present values for attributes of indicators, and ranges and priorities point out saliency” (2001: 2).
Semiotic Morphisms
Any illustration is a mapping from signified to signifier. A semiotic morphism is exactly this: a structure-preserving map from one sign-system to a different. As an alternative of signifieds we’ve a supply area, whereas as an alternative of signifiers we’ve a goal area. Understanding takes place as a course of from goal to supply, whereas design proceeds from supply to focus on (Goguen & Harrell, 2005a: 88).
Algebraic semiotics begins from the concept we are able to consider and evaluate morphisms by how properly they protect construction. rationalization or design is all about making it straightforward to translate from one system (e.g. phrases) to a different (the best way to do one thing). The sorts of construction to be preserved from one sign-system to a different are simply the elements talked about earlier than (Harrell, 2013: 147):
- Constructor-preserving – every accommodates the entire identical parts
- Operate-preserving – all operations are current in each areas
- Axiom-preserving – each programs keep the identical guidelines
- Stage-preserving – part-whole relationships are maintained
- Precedence-preserving – relative significance of parts are the identical
Therefore semiotic morphisms map kinds to kinds, subsorts to subsorts, constructors to constructors, and so forth, from supply to focus on (Goguen & Harrell, 2005a: 88). The sign-systems needn’t be precisely the identical, however ought to have corresponding construction. That’s, morphisms translate “from the language of 1 signal system to the language of one other, as an alternative of simply translating the concrete indicators within the fashions” (1999: 256). Likewise, these mappings are partial, since we are able to’t count on to maintain each single aspect, and our degree and precedence orderings assist us determine which losses matter.
Since a lot of design entails selecting to protect one factor or the opposite, Goguen recognized a number of rules by way of detailed psychological and linguistic experiments (2001: 3):
- It’s extra vital to protect construction than content material
- It’s extra vital to protect degree than precedence
- Construction and content material at decrease ranges ought to be sacrificed in favor of these at larger ranges
- Decrease degree constructors ought to be sacrificed in favor of upper degree constructors
- It’s extra vital to protect high-level kinds than priorities (Goguen & Harrell, 2005a: 96)
These outcomes are undoubtedly non-obvious, and permit a principled method to many design issues in any other case missing strong pointers. Whereas most design might be performed properly with out algebraic semiotics, the formalism actually shines in resolving tough choices (2001: 4). One instance of those rules in motion was designing a proof assistant to be extra pedagogically-friendly, which discovered that “early designs…had been incorrect as a result of the corresponding semiotic morphisms didn’t protect sure key constructors” (Goguen & Lin, 2001: 31). In a setting like instructing the place college students have vastly completely different intuitions, it might repay to take a extra summary view to accommodate everyone.
Conceptual Mixing
The best approach to perceive one thing we don’t know is by analogy with one thing we do know. As soon as there have been no phrases for ‘pc virus’ or ‘roadkill’, so we simply blended present ideas.
A technique to consider analogy is ‘conceptual areas’, formalized as units of parts with relations amongst them. A mixing is then only a mapping from one conceptual area to a different. Metaphoric blends are barely extra attention-grabbing, in that they’re uneven: in saying “the solar is a king”, we don’t evoke each high quality of a king (crown, taxes), solely probably the most salient ones. The literature even identifies optimality rules to guage whether or not a mix is nice or not (Goguen & Harrell, 2005b: 5).
This all sounds acquainted. In actual fact, we are able to see that this framework is sort of impoverished in comparison with semiotic morphisms: parts and relations usually are not typed, nor are there capabilities or axioms (ibid.).
Varieties, as an illustration, give us data like if a metaphor is a personification, or how ‘far aside’ are the weather being in contrast. Likewise, capabilities and axioms assist account for construction, resembling how a poetic meter blends with a rhyme scheme (Goguen & Harrell, 2004: 51). Most attention-grabbing of all, this enriched ‘structural mixing’ might be elegantly formalized as pushouts in class concept.
Within the easiest case of conceptual mixing we’ve a base area G (which stands for ‘generic area’) plus two enter areas ????₁ and ????₂. Right here G,????₁,????₂ and their morphisms G→????₁, G→????₂ make up the ‘enter diagram’. Likewise, a blendoid is an area B with morphisms ????₁→B, ????₂→B and G→B referred to as injections. The principle factor we wish is symmetry, the place every aspect of G will get mapped to the identical aspect of B no matter whether or not we select G→????₁→B, G→????₂→B, or G→B, i.e. the diagram commutes.
In English: ????₁ and ????₂ are two issues being in contrast, G is what they’ve in widespread, and a mix B ought to be constant it doesn’t matter what ‘aspect’ you come from. The instinct behind pushouts is that “nothing might be added to or subtracted from such an optimum blendoid with out violating consistency or simplicity indirectly” (2004: 13). That is largely summary nonsense, so let’s do an instance.
Right here we see a structural mix for the time period ‘houseboat’, or a ship that’s used as a home. The left circle is ‘home’ (????₁), the fitting circle is ‘boat’ (????₂). The underside circle is their widespread parts (G), particularly that they embrace an individual, and are on a sure medium. In the event you verify ????₁ or ????₂, every provides specifics for its enter. And naturally, on the high we’ve the mix ‘houseboat’ (B). Be aware that for the thing, particular person, and their relation, B combines from each inputs; but, for the medium we solely have ‘water’ — which is okay, as a result of we solely want weak equality, the place every aspect maps to a different.
Nonetheless, we are able to think about different doable mappings, like ‘boathouse’ (a shelter for a ship). Goguen truly needed to create a brand new categorical idea for this (‘3/2-pushouts’), for the reason that output will not be distinctive. Nonetheless, ideally we’d prefer to have guidelines in order that a pc can inform which blends make sense and which don’t.
Therefore, Goguen & Harrell (2005b) wrote a pc program to generate all doable blends for this instance. To their shock, there’s truly quite a bit — particularly 2^{A}P, the place A is the variety of axioms, and P is the variety of main blendoids. So far as I can inform, A=4 and P=3, giving 48 doable blendoids.
To slender these down, they seemed for optimality rules. The principle problem is that to automate these, they should be totally formal, primarily based on construction slightly than which means. Goguen & Harrell (2004: 52-3) in the end arrived at levels of commutativity (i.e. how a lot the arrows are ‘equal’), diploma of axiom preservation (i.e. how properly blends comply with the principles), and quantity of sort casting for constants (i.e. whether or not a blendoid has an unnatural sort). General, they’re happy that these rules match our instinct of how a lot a mix appears ‘boat-like’ or ‘house-like’ (Goguen & Harrell, 2005b: 16).
This instance was quite simple, and it seems we are able to additional generalize from pushouts to colimits. Colimits “seize the notion of ‘placing collectively’ objects to type bigger objects, in a manner that takes account of shared substructures” (2005: 62, fn. 14). They provide an optimum mix in that “they put some elements collectively, figuring out as little as doable, with nothing left over, and with nothing primarily new added” (1999: 279). As earlier than, we weaken these to ‘3/2-colimits’. In brief, they’re a robust software each to mix meanings and to review the impact of context on which means (1997: 12).
On the conceptual finish, this formalism lets us consider ‘model’ as a alternative of mixing rules, and provides us a brand new language for stylistics. Notably, many creative works make use of disoptimization rules, creating unique concepts by violating our expectations (Goguen & Harrell, 2004: 56). Extra whimsically, Goguen curated a ‘semiotic zoo’ of dangerous design decisions illustrating semiotic rules. (Sadly they’re all extraordinarily ’90s.) Whereas these examples are evocative, we don’t fairly have a common concept — no less than not till we prolong our formalism to embody sign-dynamics.
Hidden Algebra
The mathematics of algebraic semiotics is carefully associated to formal verification, or proving that software program is bug-free. One drawback with that is that almost all code is written in a rush to fulfill deadlines, typically with last-minute design modifications, and simply isn’t well worth the hassle of verifying. Typically we solely wish to know a design works (e.g. a cryptographic protocol) and go away the code as much as the person. That is referred to as formal specification, the place we show properties of designs, versus code (1997: 10).
In a static design, we wish to know the completely different components and what they do, which is like an algebra with parts and operations. Nevertheless, in dynamic designs an operator typically relies on a state that modifications over time. A pleasant instance is undo
, which fits again to the state earlier than the final command, so the pc must have the final state on file, to entry it if wanted (1999: 272).
The motivation for hidden algebra was to formalize object-oriented software program (Goguen & Malcolm, 2000: 56), by which ‘objects’ have varied attributes put collectively (e.g. an individual’s identify and peak), seen to different objects. Every object additionally has a ‘hidden’ inside state that different objects can modify by way of strategies (capabilities). Thus we’ve a division between attributes that keep the identical, and states that may change. Hidden algebra is all about dealing with each of those without delay.
Whereas seen attributes are straightforward to deal with with algebra, we are able to solely discover out a state by performing an experiment on it. This leads naturally to the concept two designs are ‘equal’ in the event that they behave the identical in all related experiments (Goguen & Lin, 2000: 28). For instance, sensible software program typically doesn’t comply with its specification precisely, so we might wish to show whether or not this makes any distinction (1997: 10). Likewise, this will help if wish to simplify a UI design with out dropping performance.
Classical semiotics takes indicators as given, however in UI design we’d like to consider indicators that change in response to person enter, or that transfer on their very own (2004: 22). Likewise, real-world signal programs are dynamic: phrases change their which means, new phrases are launched, previous phrases disappear, and even syntax modifications (1999: 272). It’s widespread to bash structuralism for being static, however and not using a formalism to explicitly specific altering states, ‘post-structuralist’ semiotics is not any higher.
This type of evaluation for behaviours of hidden states known as coalgebra, a ‘twin’ to regular algebra. Even ignoring the technical particulars, Goguen makes a powerful case that any dynamic semiotics have to be coalgebraic, and hidden algebra’s energy comes exactly from combining algebra with coalgebra.
Probably the most elaborate software to this point has been Triantafyllou et al. (2014) utilizing algebraic semiotics to measure high quality of video annotations. Goguen envisioned a type of algebraic engineering for sign-systems (Goguen & Malcolm, 1999: 164), and made spectacular progress in laying its foundations. Nonetheless, for this to truly catch on, it ought to convey not solely new formalisms, but in addition radical new concepts.
Polymorphic Poetics
Polypoems use algebraic semiotics in a generative approach to create interactive artworks. Goguen was particularly thinking about computational narratology, so the time period isn’t restricted to poetry by any means. Yet one more poetic instance is “November Qualia”, which is actually a poem constructed from randomized phrases, very like Queneau’s Hundred Thousand Billion Poems. Different proposed functions embrace pc video games that generate a plot as they’re performed (Goguen & Harrell, 2004: 49), computer-generated hip-hop (Goguen & Harrell, 2005b: 23), and varied elaborate multimedia initiatives that — in all probability for the higher — by no means materialized (Mamakos & Stefaneas, 2013).
Conversely, polymorphic poetics is using algebraic semiotics as an analytical technique, describing how decisions of semiotic morphisms have an effect on the expression of a piece (Harrell, 2013: 150). In UI design, it “makes use of morphic semiotics to assist describe how which means ‘will get into’ computing programs” (ibid., 117). Proposed functions embrace designing new media resembling VR whose guidelines usually are not well-known, growing usability of {hardware}, and supporting non-standard customers resembling individuals with disabilities (2004: 1-2). For the semiotically-inclined reader, that is in all probability probably the most compelling concept to this point, but it surely was little developed earlier than Goguen’s surprising dying from sickness in 2016.
Some hints are there about what polymorphic poetics may need seemed like if higher theorized. Sadly, it’s clear that Goguen by no means engaged with semiotics at a graduate degree. His common concept of Peirce was that he had a triadic system of signifier, signified, and an interpretant that hyperlinks these two. He sees Saussure as having a extra dyadic system of signifier vs. signified, however his main perception is that indicators happen in sign-systems (1999: 244-5). Goguen frames his method as just like Peirce, whose semiotic triangle is ‘relational’, versus the ‘purposeful’ view of Saussure (2003: 7).
An evocative illustration of the potential for algebraic semiotics is the concept artwork capabilities by way of non-preservation of construction and violation of axioms (Harrell, 2004: 148). With a big sufficient corpus, we are able to think about establishing ‘meta-rules’ of when a violation is appropriate — and these, maybe, get violated in flip. Be aware, nevertheless, that algebraic semiotics is much less a college of thought by itself, and extra a software to formalize various readings, guaranteeing consistency and revealing construction.
In an interesting paper, Goguen & Borgo (2005) mannequin free-jazz performances as nonlinear dynamical programs, the place improvisation enacts the complicated dynamics of musical part area. Chiriţă & Fiadiero (2016) framed this by way of the lens of algebraic semiotics, making a logic without cost jazz that can be utilized to guage the way it meets listeners’ expectations, discover which music fragments are hardly reachable, and predict how an improvisation will evolve. That is by far probably the most spectacular extension of algebraic semiotics so far, and reveals the deep richness that formal strategies can convey.
A really scientific concept of indicators would have huge penalties for each discipline. For Goguen (2005), the last word scope of his mission was a ‘unified idea concept’ utilizing his concept of establishments to lift algebraic semiotics right into a rigorous concept of data illustration, superseding formal idea evaluation. These claims sound grandiose to the purpose of being crankish, however by now I hope the reader has seen that Goguen was maybe the one one who might realistically ship on this.
Conclusion
It’s clear that the instruments are in place for a proper science of indicators. Goguen’s algebraic semiotics was developed with working examples carried out in OBJ code. The principle barrier has merely been that consultants in semiotics have by no means even heard of concepts like colimits or common algebra. Once more, all of that is realizable proper now — all that’s lacking is somebody prepared to do the soiled work.
Radical concepts like ‘cognitive ergonomics’ are sometimes tossed round for promoting snake oil, however Goguen opens up the tantalizing thought that foundations for this might really exist. We will speculate on an algebraic semiotics software program added to design workflows like a debugger, optimizing person expertise and doubtlessly avoiding disastrous design flaws. We will think about a semiotic department of quite a few sciences, resembling computational biosemiotics giving us algebraic fashions of animal communication.
Overwhelmingly, semiotics is used as an educational acrolect to make sure that individuals can ‘discuss the discuss’, in addition to dressing up insipid analysis to sound radical and profound. It’s time for semiotics to lastly reside as much as its potential, because the type of unified concept that offers post-structuralists nightmares.
References
- Chiriţă, C. & Fiadiero, J. (2016). “Free Jazz within the Land of Algebraic Improvisation.” Proceedings of the Seventh Worldwide Convention on Computational Creativity, pp. 322-9
- Goguen, J. (1997). “Tossing Algebraic Flowers Down the Nice Divide.” College of California, San Diego.
- Goguen, J. (1999). “An Introduction to Algebraic Semiotics, with Software to Person Interface Design,” in Nehaniv, C. (Ed.). (1999). Computation for Metaphors, Analogy, and Brokers. Heidelberg: Springer, pp. 242-91
- Goguen, J. (2001). “In direction of a Design Principle for Digital Worlds; Algebraic semiotics, with data visualization as a case examine.” Proceedings, Digital Worlds and Simulation, Society for Modelling and Simulation, San Diego, CA, pp. 298-303
- Goguen, J. (2003). “Semiotic morphisms, representations, and mixing for interface design,” in Nijholt, A., Scollo, G. & Mönnich, U. (Eds.) (2003). Proceedings of the AMAST Workshop on Algebraic Strategies in Language Processing. AMAST Press, pp. 1-15
- Goguen, J. (2004). “Steps in the direction of a Design Principle for Digital Worlds.” Working Paper.
- Goguen, J. (2005). “What’s a Idea?” in Dau, F., Mugnier, M. & Stumme, G. (Eds.). (2005). Conceptual Buildings: Widespread Semantics for Sharing Data. Proceedings of thirteenth Worldwide Convention on Conceptual Buildings. Heidelberg: Springer, pp. 52-77
- Goguen, J. & Borgo, D. (2005). “Rivers of Consciousness: The Nonlinear Dynamics of Free Jazz,” in Fisher, L. (Ed.). Jazz Analysis Proceedings Yearbook, vol. 25. Kansas: IAJE Publications, pp. 46-58
- Goguen, J. & Harrell, D. (2004). “Fashion as a Selection of Mixing Rules,” in Argamon, S., Dubnov, S. & Jupp, J. (Eds.). (2004). Fashion and That means in Language, Artwork Music and Design. Menlo Park: AAAI Press, pp. 49-56
- Goguen, J. & Harrell, D. (2005a). “Data visualisation and semiotic morphisms.” Research in Multidisciplinarity 2, pp. 83-97
- Goguen, J. & Harrell, D. (2005b). “Foundations for lively multimedia narrative: Semiotic areas and structural mixing.” Working Paper.
- Goguen, J. & Lin, Ok. (2000). “Net-based multimedia help for distributed cooperative software program engineering.” Proceedings of the 2000 Worldwide Convention on Microelectronic Programs Training.
- Goguen, J. & Malcolm, G. (1999). “Indicators and Representations: Semiotics for Person Interface Design,” in Paton, R. & Neilson, I. (1999). Visible Representations and Interpretations. Heidelberg: Springer, pp. 163-72
- Goguen, J. & Malcolm, G. (2000). “A Hidden Agenda.” Theoretical Laptop Science 245, pp. 55-101
- Harrell, D. (2013). Phantasmal Media: An Method to Creativeness, Computation, and Expression. Cambridge, MA: MIT Press, ch. 4: “Polymorphic Poetics”
- Mamakos, C. & Stefaneas, P. (2013). “Polytropos Challenge: A Mechanism for New Media.” Symmetry: Artwork and Science 1-4. pp. 230-5
- Triantafyllou, N., Ksystra, Ok., Stefaneas, P., Kalampakas, A. (2014). “In direction of Formal Symbolize-ation and Comparability of Video Content material Utilizing Algebraic Semiotics.” Proceedings of the ninth Worldwide Workshop on Semantic and Social Media Adaptation and Personalization, pp. 48-53