From 3676d5d4e67f0d3c767673c80025699cdc4654bd Mon Sep 17 00:00:00 2001 From: Claude Date: Tue, 3 Nov 2026 16:54:04 +0000 Subject: [PATCH] Add logical argument, premise, conclusion and rule of inference mcs (CSCI 201) defines these locally. Moving them here lets mcs include them instead of keeping its own copies, per the mds/mcs consolidation plan. Logical argument and rule of inference keep their mcs ids. They were in #597 until its review asked for premise and conclusion to get their own definitions, which mcs folds into the logical-argument div. Each definition now has an example; the one for rule of inference shows a pattern that is not one (affirming the consequent), so it does not repeat the common rules, which follow in their own PR. Part of #453. Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_019xfc9pMBq15Hq3DgNBx1ox --- _proof-writing.qmd | 24 +++++++++++++++++++ _subfiles/proof-writing/_def-conclusion.qmd | 8 +++++++ .../proof-writing/_def-logical-argument.qmd | 9 +++++++ _subfiles/proof-writing/_def-premise.qmd | 8 +++++++ .../proof-writing/_def-rule-of-inference.qmd | 14 +++++++++++ .../proof-writing/_exm-logical-argument.qmd | 14 +++++++++++ .../proof-writing/_exm-rule-of-inference.qmd | 20 ++++++++++++++++ 7 files changed, 97 insertions(+) create mode 100644 _subfiles/proof-writing/_def-conclusion.qmd create mode 100644 _subfiles/proof-writing/_def-logical-argument.qmd create mode 100644 _subfiles/proof-writing/_def-premise.qmd create mode 100644 _subfiles/proof-writing/_def-rule-of-inference.qmd create mode 100644 _subfiles/proof-writing/_exm-logical-argument.qmd create mode 100644 _subfiles/proof-writing/_exm-rule-of-inference.qmd diff --git a/_proof-writing.qmd b/_proof-writing.qmd index ef7c4aff8..b79cca2f6 100644 --- a/_proof-writing.qmd +++ b/_proof-writing.qmd @@ -145,6 +145,30 @@ Let's save $\rightarrow$ (`\rightarrow`) for [convergence](algebra.qmd#def-conve {{< slidebreak >}} +{{< include mds/_subfiles/proof-writing/_def-logical-argument.qmd >}} + +{{< slidebreak >}} + +{{< include mds/_subfiles/proof-writing/_def-premise.qmd >}} + +{{< slidebreak >}} + +{{< include mds/_subfiles/proof-writing/_def-conclusion.qmd >}} + +{{< slidebreak >}} + +{{< include mds/_subfiles/proof-writing/_exm-logical-argument.qmd >}} + +{{< slidebreak >}} + +{{< include mds/_subfiles/proof-writing/_def-rule-of-inference.qmd >}} + +{{< slidebreak >}} + +{{< include mds/_subfiles/proof-writing/_exm-rule-of-inference.qmd >}} + +{{< slidebreak >}} + {{< include mds/_subfiles/proof-writing/_def-proof.qmd >}} {{< slidebreak >}} diff --git a/_subfiles/proof-writing/_def-conclusion.qmd b/_subfiles/proof-writing/_def-conclusion.qmd new file mode 100644 index 000000000..59052c33a --- /dev/null +++ b/_subfiles/proof-writing/_def-conclusion.qmd @@ -0,0 +1,8 @@ +:::{#def-conclusion} +#### Conclusion + +The **conclusion** of a [logical argument](#def-logical-argument) +$P_1, \ldots, P_n \therefore Q$ +is the [proposition](#def-proposition) $Q$. + +::: diff --git a/_subfiles/proof-writing/_def-logical-argument.qmd b/_subfiles/proof-writing/_def-logical-argument.qmd new file mode 100644 index 000000000..f0375dc09 --- /dev/null +++ b/_subfiles/proof-writing/_def-logical-argument.qmd @@ -0,0 +1,9 @@ +:::{#def-logical-argument} +#### Logical argument + +A **logical argument** is a list of [propositions](#def-proposition) +$P_1, \ldots, P_n$ +together with one more [proposition](#def-proposition) $Q$. +It is written with "so" or $\therefore$ before $Q$. + +::: diff --git a/_subfiles/proof-writing/_def-premise.qmd b/_subfiles/proof-writing/_def-premise.qmd new file mode 100644 index 000000000..e921d5456 --- /dev/null +++ b/_subfiles/proof-writing/_def-premise.qmd @@ -0,0 +1,8 @@ +:::{#def-premise} +#### Premise + +The **premises** of a [logical argument](#def-logical-argument) +$P_1, \ldots, P_n \therefore Q$ +are the [propositions](#def-proposition) $P_1, \ldots, P_n$. + +::: diff --git a/_subfiles/proof-writing/_def-rule-of-inference.qmd b/_subfiles/proof-writing/_def-rule-of-inference.qmd new file mode 100644 index 000000000..053aedb5c --- /dev/null +++ b/_subfiles/proof-writing/_def-rule-of-inference.qmd @@ -0,0 +1,14 @@ +:::{#def-rule-of-inference} +#### Rule of inference + +A **rule of inference** is a pattern of [logical argument](#def-logical-argument), +written with [propositions](#def-proposition) $P, Q, \ldots$ as placeholders, +whose [premises](#def-premise) [logically entail](#def-logical-entailment) its [conclusion](#def-conclusion) +whatever propositions are put in place of $P, Q, \ldots$. +It is written with its premises above a line and its conclusion below: + +$$ +\frac{P_1, \ldots, P_n}{Q}. +$$ + +::: diff --git a/_subfiles/proof-writing/_exm-logical-argument.qmd b/_subfiles/proof-writing/_exm-logical-argument.qmd new file mode 100644 index 000000000..a78760560 --- /dev/null +++ b/_subfiles/proof-writing/_exm-logical-argument.qmd @@ -0,0 +1,14 @@ +:::{#exm-logical-argument} +#### A logical argument + + +"If $n$ is [even](number-systems.qmd#def-even-odd), then $n^2$ is even. +$n$ is even. +So $n^2$ is even." +is a [logical argument](#def-logical-argument). +Its [premises](#def-premise) are +"if $n$ is even, then $n^2$ is even" +and "$n$ is even". +Its [conclusion](#def-conclusion) is "$n^2$ is even". + +::: diff --git a/_subfiles/proof-writing/_exm-rule-of-inference.qmd b/_subfiles/proof-writing/_exm-rule-of-inference.qmd new file mode 100644 index 000000000..eff74f198 --- /dev/null +++ b/_subfiles/proof-writing/_exm-rule-of-inference.qmd @@ -0,0 +1,20 @@ +:::{#exm-rule-of-inference} +#### A pattern that is not a rule of inference + + +The pattern + +$$ +\frac{P \Rightarrow Q, \quad Q}{P} +$$ + +is not a [rule of inference](#def-rule-of-inference). +In the row of the [truth table](#def-truth-table) where $P$ is false and $Q$ is true, +both [premises](#def-premise) are true, +by the definition of [implies](#def-implies), +but the [conclusion](#def-conclusion) $P$ is false. +For example, "if $n = 2$, then $n$ is [even](number-systems.qmd#def-even-odd)" and "$n$ is even" +are both true for $n = 4$, +but "$n = 2$" is false. + +:::