The Denotational Semantics of Programming Languages
R.D. Tennent
draft 2019-04-13
0. Introduction
This note is about a concurrent logic programming language and its rhizomic pattern-theoretic semantics.
These are introduced or revived in this note:
σCP = Stochastic Concurrent Prolog
RPT = Rhizomic Pattern Theory
RhiPE = Rhizomic Pattern[-theoretic] Environment
Earlier notes:
35. Calideas – species 0.1.1
48. Rhizomatic programming
71. σCP – Stochastic Concurrent Prolog
78. A σCP formulation of the path integral
1. σCP
See [71,78] above.
The form of the clause is
Head :- Guard | Probability / Body.
Here the convention of capitalized lexical units for logical variables is reverted to.
2. Rhizomic pattern theory (RPT)
Rhizomic pattern theory is a variant of pattern theory which replaces static components (configurations) of Grenander’s pattern theory (see [33,35,48] above) with dynamic ones, in which (diagrammatically) [see pictures below for examples]
- generators = circles (with identifiers inside)
- bonds are either of type
stream (of values) = small circles (ids outside)
unitary (a single value = small boxes
with identifiers outside - all connections (between generators and bonds) are directed arrows
- a bond has (at most) one input, but can have multiple outputs (the bond relation is equality)
- There a a grammar whereby
- each generator can be replaced by a collection of generators (thus the configuration structure is dynamic)
- a generator can split into other generators
- a generator with unitary bonds is temporary, as are unitary bonds themselves
Rhizomic pattern configurations have a biological flavor: molecules (terms) flowing through (directed) filaments connecting nodes (generators, predicates) via bonds (steam or unitary logical variables).
3. RhiPE (for σCP)
| σCP | RPT | |
| predicates | generators | |
| logical variables (streams*, unitary) | bonds | |
| terms | bond values | |
| programs | (dynamic) configurations |
* [X|Xs]
4. Coin toss examples
// Fair toss …
toss([○|Xs]) :- 0.5 / toss(Xs).
toss([●|Xs]) :- 0.5 / toss(Xs).
prints([X|Xs]) :- print(X) | prints(Xs?).
:- toss(Xs),prints(Xs?).
see Figure 1, top
// … but the ‘toss’ process can run unbounded before a ‘orint’, so …
toss([○|Xs], [ok|OKs]) :- 0.5 / toss(Xs,OKs?).
toss([●|Xs], [ok|OKs]) :- 0.5 / toss(Xs,OKs?).
prints([X|Xs],OKs) :- print(X), OKs=[ok|OKs1] | prints(Xs?,OKs1).
// alternatively
prints([X|Xs],[ok|OKs]) :- print(X) | prints(Xs?,OKs).
:- toss(Xs,[ok|OKs]),prints(Xs?,OKs).
see Figure 1, bottom
// Here, the probabilities are changing …
toss([○|Xs], [ok(P)|OKs]) :- P? / toss(Xs,OKs?).
toss([●|Xs], [ok(P)|OKs]) :- Q is 1.0-P | Q? / toss(Xs,OKs?).
prints([○|Xs],[ok(0.6)|OKs]) :- print(○) | prints(Xs?,OKs).
prints([●|Xs],[ok(0.4)|OKs]) :- print(●) | prints(Xs?,OKs).
:- toss(Xs,[ok(0.5)|OKs]),prints(Xs?,OKs).
5. (Stochastic) processes and fields
Examples:
inv(B4?,B1),inv(B1?,B2),inv(B2?,B3),inv(B3?,B1),
B1=[○|_],B2=[●|_],B3=[○|_],B4=[●|_]
inv([○|Xs], [_,●|Ys]) :- inv(Xs?,Ys).
inv([●|Xs], [_,○|Ys]) :- inv(Xs?,Ys).
see Figure 2
vs.
inv([X|Xs], [_,Y}Ys]) :- flip(X?,Y), inv(Xs?,Ys).
flip(○,●).
flip(●,○).
see Figure 3
// add probabilities to make a percolation model
inv([○|Xs], [_,●|Ys]) :- 0.3 / inv(Xs,Ys).
inv([●|Xs], [_,○|Ys]) :- 0.7 / inv(Xs,Ys).
inv([○|Xs], [_,○|Ys]) :- 0.4 / inv(Xs,Ys).
inv([●|Xs], [_,●|Ys]) :- 0.6 /inv(Xs,Ys).
// create a percolation circle
perc_circle(N) :- perc_circle(N.B,B), B = [○|_]
perc_circle(0,B,B).
perc_circle(N,B_in,B_out) :-
N>0, N1 is N-1 | perc_circle(N1,B_in,B_out1), inv(B_out1,B_out).
:- perc_circle(5).
see Figure 4
// 2×2 lattice percolation
// ○ 0
// ● 1
lattice2x2([X|Xs],[Y|Ys], [_,X1|X1s],[_,Y1|Y1s]) :-
perc2to2(X?,Y?,X1,X2), perc(Xs?,Ys?,X1s,Y1s).
perc2to2(○,○,○,○) :- 0.2 / true.
perc2to2(○,○,○,●) :- 0.2 / true.
perc2to2(○,○,●,○) :- 0.3 / true.
perc2to2(○,○,●,●) :- 0.3 / true.
perc2to2(○,●,○,○) :- 0.1 / true.
perc2to2(○,●,○,●) :- 0.5 / true.
perc2to2(○,●,●,○) :- 0.2 / true.
perc2to2(○,●,●,●) :- 0.2 / true.
perc2to2(●,●,○,○) :- 0.1 / true.
perc2to2(●,●,○,●) :- 0.2 / true.
perc2to2(●,●,●,○) :- 0.1 / true.
perc2to2(●,●,●,●) :- 0.6 / true.
Figure 1 (to-be-redrawn: tbr)
Figure 2 (tbr)
Figure 3 (tbr)
Figure 4 (tbr)
language/matter dialectics
language / matter
theory ← theoretic analysis ← hidden code
↓ ↑
program → matter compiler → object code
The passive mode is the usual scientific method of observing and theorizing. The active mode is the new engineering method of synthetic biology and programmable materials science.
2019-03-3
Language is intrinsic to matter in a way that likely goes in a different direction from linguistic philosophy’s approach of separating language from the world-in-itself. A proto-linguisticality (like the proposed proto-experientiality of panpsychism) would exist in matter at all levels. This results in a form of panlinguisticism.
Our theories (composed of sentences of human-created languages) may have a fictionalist aspect, but they are attempts to interpret the hidden code of matter.
Codical Theory
Codical Theory is the study of the dialectics of language and nature.
While languages are of our (human) creation, from the perspective of Codical Theorists, the “projection” of linguisticality upon other living (and even non-living) entities is not spurious, but the recognition that the internal “languages” of nature itself is a subject for study.
On language and nature, they are synonymically related respectively:
- language = code (code in the wide sense of programming)
There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and mathematically precise theory. — Richard Montague
- nature = matter (from materialism, all is matter)
Codical Philosophy, or Codicalism, is the dialectical monism of language and matter.
2bits, qbits, xbits, a cosmos
Entanglement on a Block sphere [phys.org][arXiv:1512.03326]
Information, Physics, Quantum: The search for links
John Archibald Wheeler
it from bit — the expression invented by John Archibald Wheeler (cf. Where the “it from bit” come from) — refers to a cosmos that is made of bits and a reality that is made of programs that operate with bits as their substrate.
2bits (the conventional computing units of 0s and 1s) combined with qbits (quantum bits, or qubits) provides the substate for quantum information processing. But information is not experience; hence there must be another type of ‘bit’ (one of experientiality): xbits.
(xbits in a first approximation are like emojis.)
Other terminology:
φbits = 2bits+qbits (physical bits: information)
ψbits = xbits (psychical bits: experience)
cf. Epicurus.
A mild polemic: Where are the theoretical psychologists to team with theoretical biologists, chemists and physicists to integrate psychical and physical science.
see also Material Semantics for Unconventional Programming
1. Consciousness, Time, and Memory, Ian Phillips
2. Pain and beauty: from the psychopathology to the aesthetics of contact, Gianni Francesetti
3. in process psychology, David Ray Griffin
4. Processual Monism: A Fresh Look at the Mind-Body Problem
cf. Experiential Physicalism (in form of Panpsychism) versus Biological Naturalism
…
Codicalism: Between realism and antirealism
Codicalism is the dialectical monism of language and matter.
Languages do not exactly ‘represent’ matter (or nature), but that doesn’t mean they should remain totally ‘ignorant” of it either. Codicalists differ from constructive empiricists (as defined below*) in that the value of “mathematical abstractions” — those of the mathematical language of current physical theories — is not as high.(Mathematical language should always be viewed as a type of fiction in its relation to nature.) But creating new (mathematical) languages that are closer to what nature is should be the goal, replacing the languages that are merely instrumental.
That codicalism is the dialectical monism of language|matter — there is a linguisticity to all matter — motivates the codicalist to move from pure antirealism to a more realistic view of the relation between language and nature, even if the skepticism of exact representation should always remain.
— Bas C. van Fraassen
Histories Of Phenomenally Everything (HOPE)
or Everything Histories (EH)
Perhaps…we must also give up, by principle, the space-time continuum. It is not unimaginable that human ingenuity will some day find methods which will make it possible to proceed along such a path. At the present time, however, such a program looks like an attempt to breathe in empty space.
— Albert Einstein
In a HOPE-ful ontology, histories are fundamental entities of a quantum spacetime universe.
- There are possible histories and actual histories. Possible histories reenforce or interfere with each other (via the path integral).
- Histories replace particles and fields, which are defined in terms of ensembles of histories. Histories have physical properties, so a particular history can be an ‘electron’ history, for example.
- Histories have a path representation as a sequence going backwards in time. An element of the path sequence could be (στ,φ), where στ is a spacetime parameter (a cell or tile in quantum spacetime vocabulary — or spacicle) and φ is a physical parameter.* The reverse paths (going forward in time) are called futures. In a biverse (reflective path integral universe), retrocausality could be a feature.
- Underspecified above: The type of path (sequence) and στ; how histories interact.
* In a panpsychist theory, it would be (στ,φ,ψ), or (στ,φψ), where ψ is the psychical parameter.
HOPE can also be Histories Of Practically Everything.
29 Jan 2019
By “historical paths (curves or walks)”, “Histories have a path representation as a sequence”, I mean sequence in terms of having a linearly ordered index I, so each element of the history is indexed:
(στ,φ)ᵢ i ∈ I
22 Feb 2019
The indexing above could be t ∈ T to signify time (apart from the internal time of the στ parameter. The linearly ordered nature (discrete of continuous) just means that one thing happens before another.
Each history {(στ,φψ)ᵢ:i ∈ I} is called a storicle. The psychical parameter ψ plays a role in the (temporal) experience of the storicle.
All of reality is a collection of storicles in quantum spacetime.
2109-03019
Quantum spacetime can be viewed as a configuration of interlocking rubber tiles (spacicles).
Particles interact – via spacitons (gravitons) – with spacicles via their mass, distorting them. A sufficient mass will stretch spacicles, a stretching that propagates to neighboring spacicles resulting in a curved spacetime.
Matter gets psyched
Panpsychism may be the craziest theory of consciousness, except for all the others.
“In philosophy, hyle (from Ancient Greek: ὕλη) refers to matter or stuff.”
from Laruelle: A Stranger Thought, by Anthony Paul Smith (a book about François Laruelle)
Henry’s recasting of a radical phenomenology has been predicated on directing his analysis way from the eidos (essence, idea, form) and toward the hyle (matter, stuff) – see Michel Henry, Material Phenomenology.
If ὕ – the first Greek letter for “hyle”, upsilon (υ) with diacritics dasia and oxia (U+1F55) – is used for the symbol of matter, φ (phi) for physical, + ψ (psi) for psychical, then
(i.e., the combination of physical and psychical properties is a more complete view of what matter is). The physical is the (quantitative) behavioral aspect of matter – the kind that is formulated in mathematical language in current physics, for example – whereas the psychical is the (qualitative) experiential aspect of matter, at various levels, from brains on down. There is no reason in principle for only φ to the considered by science and for ψ to be ignored by science.
Adopting γ (gamma) for the symbol for language (γλώσσα), then codicalism
(code = κωδικός) is a dialectical monism: a dialectical monism of language and matter – not mind and matter, because matter has psychical properties in itself. Consciousness (mind) is not a mystery. Matter is.
Note: Panpsychism can be called experiential materialism. Physicalism is the (restricted) view that matter is physical, whereas experiential materialism (or as Gaylen Strawson has called it, real materialism) is the view that matter is both physical (as defined by conventional physics) and psychical (or experiential).
The alternatives to panpsychism – emergentism, informationism, illusionism – are all more problematic.
In my view there is certainly a lot of physical theory for “lower” level material things, but no physical theory yet for why “higher” level brains have consciousness. So panpsychism (psychical theories of matter) is a viable path given the failure of (magical, to me) emergentism.
24 Jan 2019
Emergentism is the view that all theories or aspects of matter – from psychical (e.g., conscious human brains), to biological, to chemical, down to particle – can all be formulated or arise somehow from the Standard Model of Particle Physics (perhaps with General Relativity, if needed), the basic physical theory. There is already a problem with emergentism: How does organic chemistry and biology ,and then up to conscious human bfians arise from the Standard Model?
Informationism is the view that consciousness is a property of complex networks of information processing elements and is substrate-independent. It isn’t clear how a planet-sized network of Intel chips could be conscious.
Panpsychism is the view that there are psychical theories or aspects – as well as physical aspects – of matter down from neurobiological to cellular to molecular, and even perhaps to atomic. Given that emergentism and informationism are likely dead ends, panpsychism is a viable approach.
25 Jan 2019
Viewing material = physical + psychical (which includes consciousness) can br “expanded” (or “complicated”) by viewing
material = physical + chemical + biological + psychical
for those for whom chemical and/or biological reductionism to physics (here physical equates to that which reduces to physics) is an issue.
Codicalism is the dialectical monism of language and matter:
κ = γ|ὕ
code = κωδικός
language = γλώσσα
hyle (matter, stuff) = ὕλη
Matter is the combination of physical and psychical:
ὕ = φ+ψ
physical = φυσικός
psychical = ψυχική
31 Jan 2019
In a micropsychist* approach, the lowest-level psychical properties could appear in the form of their own material subatomic entities, like quarks — quirks? — in current physical theories. Thus human-level consciousness is “constituted” from lower-level material entities possessing lower-level psychical features.
According to constitutive micropsychism, the smallest parts of my brain have very basic forms of consciousness, and the consciousness of my brain as a whole is in some sense made up from the consciousness of its parts. This is the form of panpsychism that suffers most acutely from the combination problem, which we will explore below. However, if it can be made sense of, constitutive micropsychism promises an elegant and parsimonious view of nature, with all the richness of nature accounted for in terms of facts at the micro-level.
* Panpsychism (SEP)
Anti-panpsychists gravitate toward emergentism (see SEP article above for its problems) or illusionism, e.g.:
Rather than thinking that this is a fundamental property of all matter, I think that it is an illusion. As well as senses for representing the external world, we have a sort of inner sense, which represents aspects of our own brain activity. And this inner sense gives us a very special perspective on our brain states, creating the impression that they have intrinsic phenomenal qualities that are quite different from all physical properties. It is a powerful impression, but just an impression. Consciousness, in that sense, is not everywhere but nowhere. Perhaps this seems as strange a view as panpsychism. But thinking about consciousness can lead one to embrace strange views.
— Keith Frankish
On the other hand,
According to the fusion view … when micro- or protoconscious entities come together in the right way, they fuse or “blend” together to form a single unified consciousness. …
— Hedda Hassel Mørch
cf. the blending of psychical (“soul”) atoms and physical atoms according to Epicurus
