--- title: "Quantum States and Disjunctive Attacks in Talmudic Logic (2016)" description: "This paper is part of a book series that formalises Talmudic reasoning and brings its ideas into general logic and AI. It gives a… 8 references." authors: ["Michaël Abraham", "Israel Belfer", "Uri J. Schild", "Dov M. Gabbay"] year: 2016 venue: "Open Repository and Bibliography (University of Luxembourg)" source: "https://orbilu.uni.lu/handle/10993/31413" licence: "Author/repository copy, free to read, no open licence — read only (no licence on the copy: author copy, read only; copy from orbilu.uni.lu)" summary_licence: "Elamur Cosmic License" canonical: "https://research.elamur.ai/free/en/papers/abraham-2016-quantum-states-disjunctive-attacks/" --- [Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/abraham-2016-quantum-states-disjunctive-attacks/) [home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [2016](https://md.research.elamur.ai/free/en/papers/2016/page/6/) / Quantum States and Disjunctive Attacks in Talmudic Logic # Quantum States and Disjunctive Attacks in Talmudic Logic **Authors:** [Michaël Abraham](https://md.research.elamur.ai/free/en/authors/michael-abraham/), [Israel Belfer](https://md.research.elamur.ai/free/en/authors/israel-belfer/), [Uri J. Schild](https://md.research.elamur.ai/free/en/authors/uri-j-schild/) and [Dov M. Gabbay](https://md.research.elamur.ai/free/en/authors/dov-m-gabbay/) · **Year:** 2016 · **Venue:** Open Repository and Bibliography (University of Luxembourg) · **Licence:** Author/repository copy, free to read, no open licence — read only (no licence on the copy: author copy, read only; copy from orbilu.uni.lu) **Links:** [Publisher's page](https://orbilu.uni.lu/handle/10993/31413) · [PDF](https://orbilu.uni.lu/bitstream/10993/31413/1/ifcolog00009.pdf) · [OpenAlex](https://openalex.org/W2626800630) **Citations:** 1 citations (OpenAlex, 2026-10-14) ## Summary This paper is part of a book series that formalises Talmudic reasoning and brings its ideas into general logic and AI. It gives a logical model for the twelfth monograph, on fuzzy logic and quantum states. The central case is a disjunctive attack: an attack on a set of arguments that hits "one of them" without singling out any member. The motivating stories are about donations and betrothals. A man commits a painting to one of two museums, or one of two paintings to a museum, or one of his daughters in marriage, and dies before choosing. The authors contrast two readings of such cases: - **Superposition view.** The commitment is spread over all candidates. - **Probabilistic view.** A choice was made but is unknown, so the uncertainty is purely epistemic. The superposition reading is captured in abstract argumentation with four labels: in, out, und and a new "wave" label. The authors then state Bochman-style axioms. Under these, a disjunctive attack either collapses onto exactly one target or puts the whole set into superposition. The wave status then passes to whatever the set attacks. The paper's contribution is to tell apart indeterminacy that exists in the world from mere ignorance about it. ## Key points - The Talmudic source is Talmud Bavli, Kidushin 51a. The two positions are Rava's (no deal, the museum gets nothing) and Abayei's (a valid deal whose object is in doubt, which the parties must undo or settle). - The labelling uses four values {in, out, und, wave}. This extends the earlier disjunctive-attack framework in reference [6]. - The two key properties are P1 and P2: - **P1:** an attack on H either collapses to attacking exactly one member, or no proper subset of H is attacked (superposition). - **P2:** wave status spreads through further attacks made by members of H. - The properties are axiomatised as AP1 and AP2. These sit alongside base axioms such as monotonicity, symmetry, affirmativity and locality. - The authors reply to two referee objections: - **Proposed new connective Q(H).** They argue a quantum state should arise only from the nature of an attack. Q would also allow a single-element set to become a wave, which yields a different logic. - **Parallel-computation reading** (from Schumann's work). They reject it because the difficulty is entanglement of states, not the order of computation. ## Interesting ideas - The paper separates two kinds of "one of N" uncertainty. In one, a choice was never made, so the commitment is genuinely shared. In the other, a choice was made but the record is lost, so probability or majority arguments apply. - A dedicated "wave" status is distinct from undecided and spreads to everything the uncertain items affect. This makes the reach of an unresolved ambiguity explicit rather than silently picking a branch. - A set-level attack is allowed only two outcomes: collapse to exactly one member, or the whole set stays superposed, with no partial subsets. This is a clean, checkable constraint on ambiguity resolution. - Pairs of scenarios differ in a single feature: an unknown donated painting among many may be sold by majority reasoning, while an undecided one blocks every sale. This minimal-pair style exposes exactly which factor changes the verdict. - Superposition can be collapsed afterwards by an explicit arbitrary act, such as a coin flip or a court decision, which is recorded as such. ## For Mova How these ideas could serve Mova, our small open language model — its files, stages and tests: - **I1** (world): when a text leaves a referent or holder open ("he gave one of his paintings"), the world model could tag it as undecided-in-world or unknown-to-reader and reason differently about each. - **I2** (frames): an unresolved coreference or role assignment could pass a "superposed" flag to the frames that depend on it, so every downstream inference shows it rests on an open ambiguity. - **I3** (tree): a resolver for PP-attachment or coordination ambiguities could be required to commit to one head or keep the full candidate set, which makes its decisions easier to audit and explain. - **I4** (learn): build evaluation and negative-control items as such minimal pairs, so a reader that ignores the decided/undecided distinction fails visibly. - **I5** (answer): when a question needs a definite answer over an unresolved world state, the reader could state that it is choosing by convention and explain that choice, instead of inventing a fact. *Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.* ## Institutions - [University of Luxembourg](https://md.research.elamur.ai/free/en/universities/university-of-luxembourg/) — University, Luxembourg, Luxembourg · 30 works · 338 citations 📚 Shelves (5): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 19,503 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 18,805 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 17,959 works · [🧮 Computational Theory and Mathematics](https://md.research.elamur.ai/free/en/shelves/computer-science/computational-theory-and-mathematics/) · 496 works · [🤔 Philosophy](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/philosophy/) · 291 works 🧭 Topics (1): [🕎 Hebrew & Aramaic](https://md.research.elamur.ai/free/en/topics/hebrew-aramaic/) · 502 works ## Cite Cite as: Michaël Abraham, Israel Belfer, Uri J. Schild and Dov M. Gabbay. 2016. Quantum States and Disjunctive Attacks in Talmudic Logic. Open Repository and Bibliography (University of Luxembourg). The paper itself, not this page. BibTeX from the library's record of the work. ```bibtex @inproceedings{abraham2016quantum, title = {{Quantum States and Disjunctive Attacks in Talmudic Logic}}, author = {Michaël Abraham, Israel Belfer, Uri J. Schild and Dov M. Gabbay}, booktitle = {Open Repository and Bibliography (University of Luxembourg)}, year = {2016}, url = {https://orbilu.uni.lu/handle/10993/31413} } ``` - [← previous Patrons sémantiques pour l'extraction de relations entre termes - Application aux comptes rendus radiologiques (Here the title in English)](https://md.research.elamur.ai/free/en/papers/ramadier-2016-patrons-semantiques-pour-l-extraction/) - [next → Review of Eli Hinkel (ed.), Teaching English Grammar to Speakers of Other Languages, Routledge, 2016.](https://md.research.elamur.ai/free/en/papers/jensen-2016-review-eli-hinkel-ed-teaching/) - [↑ back to papers of 2016](https://md.research.elamur.ai/free/en/papers/2016/page/6/) ## References 8 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet. 1. M. Abraham, I. Belfer, D. Gabbay, and U. Schild. Principles of Talmudic Logic. College Publications, 2013. [find](https://scholar.google.com/scholar?q=M%2E+Abraham%2C+I%2E+Belfer%2C+D%2E+Gabbay%2C+and+U%2E+Schild%2E+Principles+of+Talmudic+Logic%2E+College+Publications%2C+2013%2E) 2. M. Abraham, I. Belfer, D. Gabbay, and U. Schild. Fuzzy Logic and Quantum States in Talmudic Reasoning. College Publications, 2015. [find](https://scholar.google.com/scholar?q=M%2E+Abraham%2C+I%2E+Belfer%2C+D%2E+Gabbay%2C+and+U%2E+Schild%2E+Fuzzy+Logic+and+Quantum+States+in+Talmudic+Reasoning%2E+College+Publications%2C+2015%2E) 3. A. Bochman. Collective argumentation and disjunctive logic programming. J. Logic and Computation, 13(3):405–428, 2003. [find](https://scholar.google.com/scholar?q=A%2E+Bochman%2E+Collective+argumentation+and+disjunctive+logic+programming%2E+J%2E+Logic+and+Computation%2C+13%283%29%3A405%E2%80%93428%2C+2003%2E) 4. M. Caminada and D. M. Gabbay. A logical account of formal argumentation. Studia Logica, 93(2-3):109–145, 2009. [find](https://scholar.google.com/scholar?q=M%2E+Caminada+and+D%2E+M%2E+Gabbay%2E+A+logical+account+of+formal+argumentation%2E+Studia+Logica%2C+93%282%2D3%29%3A109%E2%80%93145%2C+2009%2E) 5. R. Feynman, R. Leighton, and M. Sands. The Feynman Lectures on Physics, volume III, chapter 1. Addison Wesley, Reading, 1965. [find](https://scholar.google.com/scholar?q=R%2E+Feynman%2C+R%2E+Leighton%2C+and+M%2E+Sands%2E+The+Feynman+Lectures+on+Physics%2C+volume+III%2C+chapter+1%2E+Addison+Wesley%2C+Reading%2C+1965%2E) 6. D. Gabbay and M. Gabbay. Disjunctive attacks in argumentation networks, part 1. Logic Journal of the IGPL, 24(2): 186–218, 2016. doi: 10.1093/jigpal/jzv032 First published online: September 10, 2015. [↗](https://doi.org/10.1093/jigpal/jzv032) 7. Andrew Schumann. Preface. History and Philosophy of Logic, 32(1):1–8, 2011. doi = 10.1080/01445340.2010.506079. [↗](https://doi.org/10.1080/01445340.2010.506079) 8. Andrew Schumann. Qal wa-omer and theory of massive-parallel proofs. History and Philosophy of Logic, 32(1):71–83, 2011. doi = 10.1080/01445340.2010.506104. Received June 2015 [↗](https://doi.org/10.1080/01445340.2010.506104) *Updated 4 November 2026*