AŠELYOM Volume VI — Logic, Knowledge, and Discourse

Edition 2.6 1. Purpose Grammar allows clauses to connect. Logic asks whether the connection is justified. A speaker may claim: Two propositions are both true At least one proposition is true One proposition excludes another One condition is required for another One condition is sufficient for another Two statements are equivalent A conclusion follows from stated premises A general rule applies to every member of a set An exception disproves a universal claim Two reports contradict one another A cause is being inferred from evidence These relations require more than fluent wording. The central principle is: A clear sentence may still contain weak reasoning. Logic must reveal not only what is claimed, but why the claim is allowed to follow.

1. Relational Truth and Logical Truth It does not treat relationship as permission to weaken truth. Two participants may remain in relationship while: Disagreeing Correcting one another Rejecting a false claim Requesting evidence Identifying contradiction Refusing an invalid conclusion Likewise, a formally valid argument may still be used cruelly or irresponsibly. Logical integrity and relational integrity must remain connected without becoming identical.

1. Proposition A proposition is a clause presented as capable of being: Affirmed Denied Confirmed Uncertain Unknown Conditional Hypothetical Contradictory with another proposition Examples: Dorel-om koren. The system repair is complete. Ne-om dorel koren. The system repair is not complete. Hei dorel-om koren paya dava. The system repair may be complete tomorrow. Only the first two directly oppose one another within the same time and scope.

1. Proposition Scope A proposition’s meaning depends upon its scope. Scope may include: Time Place Participant Definition Measurement method Legal jurisdiction Consent boundary Comparison set Evidential source Technical tolerance Two statements should not be declared contradictory until their scopes are aligned.

1. Same-Scope Requirement Consider: Dorel-om koren eren dava. The system repair was complete yesterday. Ne-om dorel koren nu. The system repair is not complete now. These statements may both be true if the system failed again. They differ in time. A contradiction requires the same: Proposition Meaning Reference Time Scope Standard 6. Foundational Claim States The practical claim states are: Form Meaning kare Confirmed or correct within the stated scope ne kare Incorrect or denied within the stated scope ænareya Uncertain ne nareþ Unknown or not established ili Conditional; not asserted as presently true hei Possible varel Expected or predicted A proposition may be grammatically clear while remaining evidentially uncertain.

1. Truth and Confirmation

The form kare confirms a proposition within a defined scope.

Example:

Kare · dorel-om koren nu.

Confirmed: the system repair is complete now.

This does not mean the proposition is eternally true.

The confirmation remains limited by:

Current evidence

Defined completion criteria

Time

Measurement accuracy

Scope

1. Denial and Falsity

The form ne kare denies exact confirmation.

Example:

Ne kare · dorel-om koren.

The claim that repair is complete is not correct.

A fuller correction is preferred:

Ne-om dorel koren · tirem-ar nu.

Repair is not complete; testing is underway.

Denial should offer the corrected state when known.

1. Formal Logic Register computational, and philosophical work. The standard international symbols remain available: Symbol Logical Function Native Correspondence ¬ Not ne ∧ ai ∨ Inclusive or oya ⊕ Exclusive or kare an oya → If–then implication ili … sori … ↔ Two-way equivalence Two opposed implications ∀ For all alema ∃ At least one exists anem ∄ None exists = Equal kare sami ≠ Not equal ne sami Formal notation does not replace natural-language explanation when people must act upon the result.

1. Proposition Labels Formal analysis may assign neutral labels: P — proposition P1, P2, P3 — numbered propositions C — conclusion D — defined domain E — evidence statement Example: P1: If pressure exceeds 300 kPa, the system stops. P2: Pressure exceeds 300 kPa. C: The system stops. Labels help expose structure without adding new lexical roots prematurely.

1. AI — Logical Conjunction

The linker ai may mean that both propositions are affirmed.

Formal correspondence:

P ai Q

P∧Q

Example:

Dorel-om koren ai tirem-om norel.

The system repair is complete, and the water measurement is complete.

The combined proposition is confirmed only if both clauses are confirmed.

1. Conjunction Truth

For a conjunction:

P ai Q

the complete claim fails if either P or Q fails.

Example:

Claim:

The pump is stopped and the valve is closed.

If the pump is stopped but the valve remains open, the full conjunction is false.

A partial truth must not be reported as complete confirmation.

1. Conjunction and Shared Responsibility

Conjunction joins claims.

It does not merge participants.

Example:

Dorel-en Mark koren ai tirem-en Skylar norel.

Mark repaired the system, and Skylar measured the water.

The sentence does not imply both participants performed both actions.

1. Conjunction and Collective Claims

Example:

Alema sena velor-ar ai kare nareþ-om ni scope.

All participants consent, and the scope is clearly understood.

Both conditions may be required.

The presence of one does not compensate for the absence of the other.

1. OYA — Logical Disjunction The linker oya presents alternatives. By default: P oya Q means: P may be true Q may be true Both may be true This is inclusive disjunction. Formal correspondence: P∨Q 16. Inclusive Alternative Example: Vel jora tu tirem oya dorel. The listener may perform measurement, repair, or both. If both actions are prohibited from occurring together, the sentence must state that restric‐ tion.

1. Exclusive Alternative

Exactly one alternative is marked through:

kare an oya

Formal correspondence:

P⊕Q

Example:

Kare an oya · jora path east · jora path west.

Choose exactly one: the east path or the west path.

The structure excludes choosing both.

1. Complete Alternatives

A choice should state whether the listed alternatives are complete.

Example:

Diri option va ni complete set?

Which option within the complete set?

When other possibilities may exist, the speaker should not present two options as exhaustive.

1. False Dichotomy

A false dichotomy presents two options as though no others exist.

Example:

Either you agree with me or you oppose the community.

Possible omitted states include: Partial agreement Uncertainty Need for clarification Independent proposal Abstention Refusal of the framing itself A legitimate exclusive alternative requires an actually restricted set.

1. NE — Logical Negation

The particle ne denies the proposition within its scope.

Formal correspondence:

ne P

¬P

Example:

Ne dorel-om koren.

The system repair is not complete.

Logical negation should target the complete proposition when complete denial is intended.

1. Negating a Conjunction

The statement:

ne (P ai Q)

means:

It is not true that both P and Q are true.

This does not necessarily mean both are false.

Example:

Ne kare li dorel-om koren ai tirem-om norel.

It is not confirmed that both repair and testing are complete.

Possibilities include:

Repair complete, testing incomplete

Repair incomplete, testing complete

Both incomplete

1. Negating an Alternative

The statement:

ne (P oya Q)

means neither alternative is true when oya is inclusive.

For clarity, ordinary language should often state:

Ne P ai ne Q.

Example:

Ne vel jora telem A ai ne vel jora telem B.

Use of Tool A is not permitted, and use of Tool B is not permitted.

1. ČAREL — Contradiction The Logical Relation Form is: čarel Pronunciation /tʃɑˈɾel/ Core Meaning Two propositions cannot both be true under the same meaning, time, reference, and scope. Example: Čarel li dorel-om koren nu ma li ne-om dorel koren nu. The claims “repair is complete now” and “repair is not complete now” contradict one anoth‐ er. Anti-Definition Disagreement is not automatically contradiction. Difference in perspective, scope, time, or definition may allow both statements to remain true.

1. SAVAL — Compatibility The Logical Relation Form is: saval Pronunciation /sɑˈvɑl/ Core Meaning Two propositions may both be true within the same broader field. Example: Saval li marel-ar me te tu ma li ne velor-ar me te touch. The claims “I trust you” and “I do not consent to touch” are compatible. Compatibility does not mean the propositions support one another. It means they do not logically exclude one another.

1. Disagreement Versus Contradiction

Two participants may disagree without producing direct contradiction.

Speaker One:

Me · nareþ-ar taren-ves ni path.

I understand the path as dangerous.

Speaker Two:

Me · ænareya te taren ni path.

I am uncertain whether the path is dangerous.

The statements differ.

They are not direct logical opposites.

1. Inconsistency

A set of claims is inconsistent when all of them cannot be true together.

Example:

Every valve is closed.

Valve Three is open. If Valve Three belongs to the stated set and the terms are defined consistently, the claim set is inconsistent. An inconsistency may arise through: Error Different timestamps Ambiguous categories False reporting Changed conditions Conflicting measurements The source must be investigated.

1. Formal Noncontradiction

Within a stable formal scope:

P ai ne P

cannot both be confirmed.

Formal correspondence:

This principle applies to one proposition under the same interpretation and scope.

It does not require human experience to become emotionally simple or binary.

1. Excluded Middle In a fully defined two-valued formal system: P oya ne P exhausts the logical possibilities. However, ordinary discourse may include: Unknown data Unclear definitions Changing conditions Incomplete observation Category ambiguity Indeterminate future events Therefore, conversational answers may legitimately include: Uncertain Unknown Not yet determined The question is malformed 29. ILI–SORI — Implication The structure: ili P · sori Q means: If P is fulfilled, Q follows within the stated rule or model. Formal correspondence: P→Q Example: Ili pressure har 300 kPa · sori tam koren. If pressure exceeds 300 kilopascals, the system stops.

1. Implication Is Not Cause The rule: If the alarm sounds, the building is evacuated does not mean the alarm physically causes every person to move. It may indicate: Procedure Requirement Logical dependency Operational rule Predictive model Causal language requires a separate supported claim.

1. Sufficient Condition

Within:

ili P · sori Q

P is sufficient for Q under the stated rule.

Meaning:

Whenever P is established, Q follows.

Example:

Ili kare password ai kare token · sori vel access.

Correct password and token together are sufficient for access.

A sufficient condition may not be the only way to reach the result.

1. Necessary Condition

A condition is necessary when the result cannot occur without it.

The established natural-language structure is:

Q kare ili P

Meaning:

Q only if P.

Example:

Vel jora system kare ili authorization kare.

System operation is permitted only if authorization is confirmed.

P is necessary for Q.

1. Necessary Versus Sufficient

Compare:

Ili fire pelen-ar · sori alarm jora-ar.

If fire emerges, the alarm activates.

Fire is stated as sufficient for alarm activation.

This does not prove alarm activation always means fire.

Another condition may also activate the alarm.

1. Two-Way Condition

Two propositions are logically equivalent when each implies the other.

Structure:

Ili P · sori Q ai ili Q · sori P.

Formal correspondence:

P↔Q

Example:

Ili code kare · sori indicator green ai ili indicator green · sori code kare.

This is a two-way claim.

It should be made only when both directions are supported.

1. Converse

From:

P→Q

the converse is:

Q→P

The converse does not automatically follow.

Example:

If it rains, the ground becomes wet.

The converse:

If the ground is wet, it rained.

may be false because irrigation or a leak could also wet the ground.

1. Inverse

From:

P→Q

the inverse is:

ne P → ne Q

The inverse does not automatically follow.

Example:

If the heater operates, the room becomes warm.

It does not follow that if the heater is off, the room cannot be warm.

Sunlight may warm it.

1. Contrapositive

From:

P→Q

the contrapositive is:

ne Q → ne P

Within formal logic, the contrapositive is equivalent to the original implication.

Example:

If the system is operating, power is present.

Therefore:

If power is not present, the system is not operating.

This equivalence assumes the original rule is truly universal within the defined system.

1. Necessary and Sufficient Conditions A condition is necessary and sufficient when both directions hold. Example: A digital lock opens exactly when: The correct password is entered The correct hardware token is present No lockout state is active The full equivalence must include every required condition.

Omitting one condition creates a false rule.

1. NELI — Unless

The form neli establishes an exception condition.

Example:

Neli emergency pelen-ar · ke þel nalem.

Do not cross the boundary unless an emergency arises.

A clearer positive equivalent may be:

Vel þel nalem kare ili emergency pelen-ar.

Crossing is permitted only if an emergency arises.

Positive conditions are often easier to test.

1. Quantifiers A Quantifier states how much of a defined set is included in a proposition. The foundational Quantifier Forms are: Form Meaning alema All members of a defined set edem Each member considered individually anem At least one; some None; zero members meora Most members feya Few members sola Only the following member, action, or condition kare + number Exactly the stated number These forms are classified as: Founding–Experimental 41. Domain A quantifier must apply to a defined set or field. This set is called the: Domain Example: alema telem va ni set All tools within the identified set. Without a domain, the statement may become impossibly broad.

1. ALEMA — All

Core Meaning

Every member of the defined domain satisfies the proposition.

Example:

Alema telem va ni set dorel-ves.

All tools in the set are repairable.

Formal correspondence:

∀x

The claim fails if one genuine member of the domain does not satisfy the proposition.

1. EDEM — Each Core Meaning Every member is considered separately.

Example:

Edem telem va ni set tirem-en me.

This speaker measured each tool in the set.

alema emphasizes total coverage.

edem emphasizes individual application.

1. All Versus Collective Action

Compare:

Alema sena þalen-en.

All participants journeyed.

This may allow separate journeys.

Sora · þalen-en.

The participants knowingly journeyed as a shared action.

Universal participation does not automatically create Shared Voice.

1. ANEM — At Least One

Core Meaning

One or more members of the domain satisfy the proposition.

Example:

Anem telem va ni set nakor-en.

At least one tool in the set failed.

Formal correspondence:

∃x

The statement does not identify:

Which member

How many members

Whether most members satisfy the claim

1. ÆM — None

The existing zero form æm expresses that no members of the domain satisfy the proposition.

Example:

Æm telem va ni set nakor-en.

No tools in the set failed.

Formal correspondence:

∄x

A universal negative claim requires adequate observation of the full relevant domain.

1. MEORA — Most Core Meaning More than half of the defined domain satisfies the proposition. Example: Meora telem va ni set dorel-ves. Most tools in the set are repairable. A claim of “most” should be based on: Complete count Valid sample Reliable record Clearly stated estimate 48. FEYA — Few Core Meaning A small portion of the defined domain satisfies the proposition. Example: Feya telem va ni set nakor-en. Few tools in the set failed. “Few” is relative unless a threshold is defined. Technical writing should use a number or percentage.

1. SOLA — Only

The form sola restricts the proposition to the immediately following element.

Example:

Sola Mark dorel-en koren.

Only Mark repaired the system.

The restriction applies to the actor.

Example:

Mark dorel-en sola koren.

Mark repaired only the system, not another object.

Example:

Mark sola dorel-en koren.

Potentially ambiguous: Mark only repaired the system and performed no other relevant ac‐

tion.

Because scope is sensitive, sola should remain directly beside the restricted element.

1. Exactly a Number

Exact quantity uses:

kare + number

Example:

Kare sor telem nakor-en.

Exactly three tools failed.

Example:

Kare an se dorel-en koren.

Exactly one participant repaired the system.

Exact claims require complete or sufficiently reliable counting.

1. At Least and At Most Technical notation remains preferred: ≥ 3 — at least three ≤ 3 — at most three Natural-language analytical forms are: sami oya har sor Equal to or greater than three. sami oya nur sor Equal to or less than three. These constructions are precise but heavy. Technical symbols are encouraged where accessible.

1. Quantifier Scope

Compare:

Ne alema telem nakor-en.

Not all tools failed.

This means at least one tool did not fail.

It does not mean:

Æm telem nakor-en.

No tools failed.

Quantifier scope must remain visible.

1. Not All Versus None

Not All

Ne alema participants velor-ar.

Not all participants consent.

Some may consent.

None

Æm participants velor-ar.

No participants consent.

These meanings must never be confused in governance or consent records.

1. Some Versus Most

Example:

Anem participants velor-ar.

At least one participant consents.

Example:

Meora participants velor-ar.

Most participants consent.

Neither statement establishes unanimous consent.

Neither authorizes the use of sora for the entire group.

1. Universal Claim

A Universal Claim applies to all members of its domain.

Example:

Alema human beings require water.

Such claims require careful domain and condition definition.

Exceptions may reveal:

An inaccurate claim

An incorrectly defined category

A hidden condition

An abnormal case

A measurement error

1. Counterexample

A counterexample is one valid case that disproves a universal claim.

Claim:

Alema telem va ni set dorel-ves.

All tools in the set are repairable.

Counterexample:

Telem Four ne dorel-ves.

Tool Four is not repairable.

If Tool Four truly belongs to the defined set, the universal claim fails.

1. Existential Claim

An Existential Claim states that at least one qualifying member exists.

Example:

Anem telem va-horen dorel-ves.

At least one repairable tool is inside the shelter.

One confirmed example is sufficient to establish the claim.

1. Unique Existence

Unique existence combines:

At least one

At most one

Ordinary form:

Kare an telem va-horen dorel-ves.

Exactly one repairable tool is inside the shelter.

Formal notation may use:

∃!x

1. Exception

An exception may use neli or an explicit removal from the domain.

Example:

Alema telem dorel-ves neli telem Four.

All tools are repairable except Tool Four.

The exception should be named rather than hidden.

A rule with many exceptions may need revision.

1. Generalization

A Generalization extends a finding from observed cases toward a broader domain.

Example:

Five tested tools failed.

Conclusion:

All tools of that design fail.

The conclusion may be plausible.

It is not deductively guaranteed without additional evidence.

The speaker should identify:

Sample size

Selection method

Conditions

Similarity of untested cases

Confidence level

1. Overgeneralization

Overgeneralization occurs when a conclusion exceeds the available cases.

Example:

One participant broke a promise.

Invalid conclusion:

Every member of the group is untrustworthy.

The language should preserve the observed scope:

An se jora-en broken promise.

One participant broke a promise.

1. Class Membership

A Presence Form may be classified within a category.

Example:

Ram di telem ni safety-critical set.

This tool is a member of the safety-critical set.

Membership does not mean the member possesses every property loosely associated with the

category.

Only defined category rules may be inferred.

1. Classification Versus Identity

Example:

Elar se dorel-dai va ni project.

The participant serves as a repair practitioner in the project.

This is a role classification.

It does not mean the person’s total identity is “repair practitioner.”

Logical classification should not become metaphysical reduction.

1. Set Inclusion

One category may be fully contained within another.

Example:

All water pumps are machines.

Not all machines are water pumps.

Formal notation:

A⊆B

The reverse inclusion requires separate proof.

1. Category Overlap

Two categories may share some members without either containing the other.

Example:

Some stewards are repair practitioners.

Some repair practitioners are not stewards.

The overlap should not be mistaken for equivalence.

1. Disjoint Categories

Two categories are disjoint when no member may belong to both within the defined system.

Example:

A binary system state may define:

Active

Inactive

as mutually exclusive.

Real-world categories are often less clean.

The definitions must be tested rather than assumed.

1. Relations Logic may examine properties of relationships. A relation may be: Reflexive Symmetric Asymmetric Reciprocal Transitive Non-transitive One-way Many-to-one Time-limited Every relational root does not automatically share the same logical properties.

1. Symmetric Relationship

A relation is symmetric when:

If A bears the relation to B, B bears the same relation to A.

Example:

Being the same measured distance apart is symmetric.

If A is two meters from B, B is two meters from A.

1. Asymmetric Relationship

A relation is asymmetric when the reverse relation cannot hold in the same form.

Example:

If A is the legal parent of B, B is not the legal parent of A within the same relation.

Direction matters.

1. Reciprocal Relationship

A reciprocal relationship requires action in both directions.

Example:

Irel-ar matu yanem.

You and I attend to one another.

Reciprocal grammar asserts both directions.

It does not prove equal degree, intensity, or benefit.

1. Transitive Relationship A relation is transitive when: A relates to B B relates to C Therefore A relates to C Numerical “greater than” is transitive. If A is greater than B and B is greater than C, A is greater than C. Many human relationships are not transitive.

1. Non-Transitive Relationship

Trust is not automatically transitive.

If Mark trusts Skylar, and Skylar trusts Jordan, it does not follow that Mark trusts Jordan.

Consent is not transitive.

If Mark consents to Skylar, and Skylar consents to Jordan, no consent relation between Mark

and Jordan follows.

1. Argument An argument is a structured movement from supporting propositions toward a conclusion. A formal argument contains: One or more premises A rule of inference A conclusion The conclusion should not contain more certainty than the premises and inference allow.

1. Premises

A premise is a proposition offered as support.

Formal labels:

Example: P1: All tools in Set A were tested. P2: No tested tools failed. C: No tools in Set A failed during the test. The conclusion remains limited to: Set A The test interval The tested failure criteria 75. Deductive Validity An argument is deductively valid when: If the premises are true, the conclusion cannot be false. Validity concerns structure. It does not prove that the premises are actually true.

1. Soundness

A deductive argument is sound when:

The argument is valid.

Its premises are true or sufficiently established.

A valid argument with a false premise remains unsound.

Example:

P1: All blue tools are indestructible. P2: This tool is blue. C: This tool is indestructible.

The structure may be valid.

The first premise is false or unsupported.

1. Deductive Reasoning

Deduction moves from rule to necessary conclusion.

Example:

P1: Every authorized repair requires an active permit. P2: This repair is authorized. C: An

active permit is required.

Deductive reasoning depends heavily on precise definitions.

1. Inductive Reasoning

Induction moves from observed cases toward a probable generalization.

Example:

Twenty tested valves of one design failed under the same pressure.

Conclusion:

Other valves of the same design may have a high failure risk.

The conclusion is supported.

It is not logically guaranteed.

1. Abductive Reasoning

Abduction proposes the best current explanation for observed evidence.

Example:

Pressure fell rapidly.

Water appeared beneath the pipe. A leak is a likely explanation. Other explanations may remain possible. Abductive conclusions should use: varel hei ænareya Confidence measures rather than unconditional certainty.

1. Defeasible Reasoning A defeasible conclusion is reasonable under current information but may be withdrawn if new evidence appears. Example: The system is presumed operational because: Repair completed Testing passed No alarms are active A later sensor failure may defeat the conclusion. Everyday reasoning is often defeasible rather than mathematically final.

1. Probability Is Not Implication

A high probability does not create logical certainty.

Example:

There is a 90% chance of rain.

This does not imply that rain must occur.

Likewise, a low probability event may still occur.

Probability statements should use numerical or clearly defined confidence measures where

possible.

1. Correlation Correlation means two variables change together in an observed pattern. It does not by itself establish: Which variable causes the other Whether a third factor causes both Whether the pattern is accidental Whether the relation continues outside the sample The language should avoid translating correlation directly through nari.

1. Causal Claim A causal claim states that one condition contributes to producing another. Evidence may include: Controlled intervention Temporal order Mechanism Repeated observation Elimination of alternatives Dose-response pattern Domain knowledge Causation usually requires more support than mere sequence.

1. Single and Contributing Causes An event may have: One sufficient cause Several necessary conditions Several contributing causes A triggering event A background condition A human decision A system design weakness A complete account should not force every event into one-cause language.

1. Evidence Versus Conclusion Evidence is not the same as the conclusion drawn from it. Example: Evidence: The sensor reported zero flow. Possible conclusions: No water is flowing The sensor failed The pipe is blocked The sensor is disconnected The evidence supports investigation. It does not uniquely determine one conclusion without further information.

1. Burden of Support

The participant making a consequential claim should provide appropriate support.

Stronger claims require stronger support.

Examples:

“I felt uneasy” requires personal report.

“The system is unsafe” requires relevant safety evidence.

“Every member agreed” requires complete consent records.

“This action caused the failure” requires causal support.

Relational confidence does not replace evidential responsibility.

1. Absence of Evidence Failure to find evidence may mean: The claim is false The search was incomplete The instrument was inadequate The evidence was removed The phenomenon is difficult to detect The wrong location was examined Absence of evidence becomes evidence of absence only when the detection method should reliably have found the thing if it were present.

1. Hidden Premise

An argument may depend on an unstated assumption.

Example:

“The system passed inspection, therefore it is safe.”

Hidden premise:

“The inspection was complete, valid, current, and sufficient to establish safety.”

Important hidden premises should be made explicit.

1. Circular Reasoning

Circular reasoning uses the conclusion as support for itself.

Example:

The council is trustworthy because its decisions are trustworthy.

Its decisions are trustworthy because the council is trustworthy.

No independent support has been provided.

1. Equivocation Equivocation occurs when one word changes meaning during an argument. Example: “Natural” may mean: Existing in nature Minimally processed Healthy Morally good Legally unregulated An argument becomes invalid when it shifts between these meanings without acknowledg‐ ment. Anti-Definitions help prevent equivocation.

1. Person Versus Claim A claim should be evaluated through: Meaning Evidence Scope Source reliability Attacking the person does not prove the claim false. Likewise, admiring the person does not prove the claim true. A participant’s conduct may affect source reliability. It does not replace evaluation of the proposition.

1. Authority Relevant expertise may strengthen a claim. Authority does not create certainty outside its field. A speaker should identify: The expert’s domain The evidence used Agreement or disagreement among experts Currentness Conflicts of interest Limits “An authority said it” is not a complete argument.

1. Shared Voice and Logic

A Shared Voice may confirm that a group agrees.

It cannot make the proposition true merely through agreement.

Example:

Sora · kare li ni path safe-ves.

We jointly affirm that the path is safe.

The statement still requires evidence appropriate to safety.

Consensus establishes shared belief or decision.

It does not alter material conditions.

1. Emergent Voice and Logic

The Emergent Voice may offer a hypothesis.

Example:

Soreya · hei nalem-iel va-soren.

A boundary may be emerging within the shared field.

The claim may guide inquiry.

It should not be treated as deductive proof, command, or objective measurement.

1. Consent Logic

Consent requires more than the absence of refusal.

Invalid inference:

P1: The participant did not say no. C: The participant consented.

The conclusion does not follow.

A valid consent claim requires positive evidence of active consent within scope.

1. Group Logic

Invalid inference:

P1: Most members support the proposal. C: All members support the proposal.

The conclusion does not follow.

Invalid inference:

P1: The group approved the proposal by its accepted voting procedure. C: Every member

personally agrees.

Institutional decision and individual belief remain separate.

1. Stewardship Logic

Invalid inference:

P1: Mark is the steward of the system. C: Mark owns the system.

Stewardship does not imply title.

Invalid inference:

P1: Skylar holds the tool. C: Skylar may use the tool.

Physical possession does not imply permission.

1. Technical Logic Technical rules should identify: Inputs Conditions Thresholds State changes Fail-safe action Unknown-state handling Reset conditions Human authority Example: Ili pressure > 300 kPa · sori tam Pump-2. This rule should not silently assume the pressure sensor is functioning.

A separate rule must address sensor uncertainty.

1. Automation and Three-Valued States Automated systems often require more than true and false. A practical state set may include: True False Unknown Error Not applicable Not yet evaluated Unknown must not default automatically to safe, permitted, or false.

1. Legal Logic Legal rules often contain: Definitions Duties Exceptions Jurisdiction Standards of proof Deadlines Remedies Conflicting authority A legal conclusion may be valid only within a specific jurisdiction and date. Logical form should not conceal interpretive uncertainty.

1. Reflective and Spiritual Claims A reflective statement may be meaningful without operating as a formal proposition. Example: Life is Dream awakening to itself. This may function as: Metaphor Theology Mystical interpretation Literary assertion Philosophical proposal Its genre should be clear. Poetic depth should not be forced into an inappropriate scientific proof structure.

1. Formal Truth and Lived Complexity A proposition may be formally binary while the lived situation remains complex. Example: Consent may be active or inactive for one specific action. The surrounding person may simultaneously feel: Love Fear Curiosity Grief Uncertainty Attraction Distrust The logical clarity of consent does not require emotional simplicity.

1. Logic-Coherence Test Before accepting an argument, ask: Proposition What exactly is being claimed? Scope What time, domain, definition, and standard apply? Link Is the relation conjunction, alternative, contradiction, implication, equivalence, cause, or in‐ ference? Quantifier Does the claim concern all, each, some, none, most, few, or exactly a number? Evidence What supports each premise? Validity Would the conclusion follow if the premises were true? Soundness Are the premises themselves sufficiently established? Exception Would one counterexample defeat the claim? Ambiguity Has any word changed meaning during the argument? Responsibility What decision, consent, safety, or reputation depends upon the conclusion?

1. The Logic Covenant

Logical discourse follows this covenant:

A clear sentence will not be mistaken for a proven claim.

Agreement will not be mistaken for truth.

Disagreement will not be mistaken for contradiction.

Difference in scope will be checked before declaring inconsistency.

Addition will not become causation without support.

Sequence will not become cause merely because one event came first.

A conditional will not be reversed without proof.

A universal claim will remain open to counterexample.

“Some” will not become “all.”

“Most” will not become consensus.

Absence of refusal will not become consent.

Physical possession will not become permission.

Evidence will remain separate from conclusion.

Probability will not become certainty.

Formal precision will not be used to erase lived context.

1. Official Logic Rules

A proposition must be evaluated within its scope.

ai corresponds to logical conjunction.

oya corresponds to inclusive disjunction by default.

kare an oya marks exclusive disjunction.

ne marks logical negation.

čarel marks contradiction within identical scope.

saval marks compatibility.

ili P · sori Q expresses implication.

Implication does not automatically establish cause.

Q kare ili P means Q only if P.

Two-way equivalence requires both implications.

The converse and inverse do not follow automatically.

The contrapositive is formally equivalent to a valid implication.

alema marks all members of a domain.

edem marks each member individually.

anem marks at least one member.

æm marks no members.

meora marks most members.

feya marks few members.

sola restricts the element immediately following it.

kare + number marks exact quantity.

“Not all” is not equivalent to “none.”

One counterexample defeats a universal claim.

Validity concerns structure; soundness also requires established premises.

Deductive, inductive, abductive, and defeasible reasoning must remain distinguished.

Correlation is not causation.

Consensus does not establish material truth.

Formal logic does not erase ethical, relational, or evidential responsibility.

1. Founding Logic Reference Existing Logical Forms ne · ai · oya · bei · nari · sori · ili · neli · kare · æm New Logical Relations Form Meaning čarel Contradiction under the same scope saval Compatibility or co-possibility Quantifiers Form Meaning alema All edem Each anem At least one or some None meora Most feya Few sola Only kare + number Exactly the stated number 107. Sample Formal Argument Premises P1: Alema norel va ni tested containers safe-ves. All water in the tested containers is established as safe. P2: Ram Container Three ni tested containers. Container Three belongs to the tested-container set. Conclusion C: Safe-ves norel va Container Three. The water in Container Three is established as safe. The argument is valid only if: The universal premise is accurate Container Three truly belongs to the tested set “Safe” uses the same criteria throughout The test remains current 108. Sample Invalid Converse Established Rule Ili fire pelen-ar · sori alarm jora-ar. If fire emerges, the alarm activates.

Observation

Alarm jora-ar.

The alarm is active.

Invalid Conclusion

Sori fire pelen-ar.

Therefore, fire exists.

The conclusion does not follow unless fire is the only possible alarm trigger.

1. Sample Quantifier Contrast

Alema dorel-dai velor-ar.

All repair practitioners consent.

Meora dorel-dai velor-ar.

Most repair practitioners consent.

Anem dorel-dai velor-ar.

At least one repair practitioner consents.

Æm dorel-dai velor-ar.

No repair practitioners consent.

Ne alema dorel-dai velor-ar.

Not all repair practitioners consent.

Each statement creates a different decision state.

1. Sample Relational Logic

Marel-ar me te tu.

This speaker trusts the listener.

Ne velor-ar me te touch.

This speaker does not consent to touch.

Saval ni propositions.

These propositions are compatible.

Trust does not logically entail consent.

1. Sample Stewardship Logic

Sa-me norel-ker.

The water system is entrusted to this speaker’s care.

Ne loran-ar me ni.

This speaker does not hold legal title to it.

Vel tam me ni na taren.

This speaker is permitted to stop it during danger.

The stewardship relation supports limited authority without implying ownership.

1. What Is Now Established This chapter establishes: Proposition and scope Practical claim states A Formal Logic Register Conjunction and disjunction Exclusive alternatives Logical negation Contradiction and compatibility Implication Necessary and sufficient conditions Converse, inverse, and contrapositive distinctions Two-way logical equivalence Quantifier grammar Domains and set membership Universal, existential, majority, and exact claims Exceptions and counterexamples Generalization and overgeneralization Category inclusion, overlap, and disjointness Symmetric, asymmetric, reciprocal, and transitive relations Arguments, premises, validity, and soundness Deductive, inductive, abductive, and defeasible reasoning Probability, correlation, and causation distinctions Hidden premises, circular reasoning, equivocation, and false dichotomies Logical safeguards for consent, stewardship, groups, automation, law, and spiritual discourse The Logic Covenant 113. Status of Chapter 31 The logical use of these existing forms is classified as: Founding–Stable ne · ai · oya · ili · sori · kare · æm The following new Logical Relation Forms are classified as: Founding–Experimental čarel · saval The Quantifier Forms are classified as: Founding–Experimental alema · edem · anem · meora · feya · sola They require testing through: Formal logic exercises Technical procedures Consent records Legal language Group governance Statistical reporting Scientific argument Debate Everyday reasoning Spoken comprehension 114. Next Chapter

The next chapter will deepen conditional reasoning through: Real and open conditions Expected conditions Unlikely conditions Impossible conditions Past counterfactuals Present counterfactuals Future contingencies Necessary and sufficient conditions Multiple dependencies Failure branches Fallback actions Unless, except, even if, and only if Decision trees Risk thresholds Conditional permission and consent Conditional promises and obligations Plans that adapt when conditions change The immediate goal is to let the language say not merely “if this, then that,” but what kind of possibility the speaker believes the condition represents.