其他技能

First-order logic with quantifiers, predicates, functions, and identity. Covers syntax, interpretation over a domain, the universal and existential quantifiers, quantifier scope and binding, translation from natural language with multi-variable predicates, natural deduction for quantifiers, undecidability at first order, and the soundness/completeness theorems. Use when propositional logic is insufficient -- whenever "for all" or "there exists" matters to the argument.

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The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?"

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Practical argument analysis and construction -- how to identify, evaluate, reconstruct, and build real arguments in natural language. Covers argument identification (premises, conclusions, intermediate steps), charity and steel-manning, argument mapping, the distinction between deductive validity and inductive strength, burden of proof, and the rhetorical context in which arguments operate. Use when the goal is to engage with real-world argument rather than to formalize it.

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Pragmatics and communicative competence across languages -- speech acts (Austin/Searle), Grice's conversational maxims and implicature, politeness theory (Brown & Levinson), face-threatening acts, discourse structure, turn-taking, repair strategies, register and formality, cross-cultural communication, communicative strategies (circumlocution, approximation, appeal for assistance), and the gap between grammatical competence and communicative performance. Use when teaching communication skills, analyzing cross-cultural misunderstandings, building conversational fluency, or understanding why grammatically correct sentences can be pragmatically inappropriate.

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Sound systems of human language -- phoneme inventories, the International Phonetic Alphabet, articulatory and acoustic phonetics, phonological rules, suprasegmental features (stress, tone, intonation), and ear training for non-native sound perception. Covers place and manner of articulation, voicing contrasts, vowel space, minimal pair analysis, allophonic variation, phonotactic constraints, connected speech phenomena (assimilation, elision, liaison), and prosody across language families. Use when analyzing pronunciation, teaching sound systems, performing phonemic transcription, or diagnosing intelligibility problems in any language.

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Extending propositional and predicate logic with modal operators -- necessity and possibility, and their relatives (obligation, knowledge, belief, time). Covers Kripke possible-worlds semantics, accessibility relations, the main modal systems (K, T, S4, S5), translation from natural language, and applications in epistemic, deontic, and temporal reasoning. Use when ordinary logic is insufficient to capture distinctions like "must" vs "might," "knows" vs "believes," "always" vs "sometimes."

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Martial arts as body discipline — the shared pedagogical structure across striking, grappling, and weapon arts (stance, distance, timing, ukemi, live partner work, graded ranking, and the ethical container the best schools enforce). Covers karate, judo, jiu-jitsu (Brazilian and traditional Japanese), aikido, kendo/kenjutsu, boxing, muay Thai, and wrestling at enough depth that an agent can place a user into a reasonable first-month practice and recognize the safety failures that matter most. Leans on Moshé Feldenkrais's judo background and Yang Jwing-Ming's martial scholarship for the internal-to-external bridge. Use for any query about beginning a martial art, training injury patterns, graded progression, or the ethics of combat training.

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The household as an economic unit with income, expenses, savings, and debt. Covers the envelope method, fixed vs variable expenses, the 50-30-20 baseline, emergency reserves, the true cost of ownership, opportunity cost in household decisions, and the distinction between a budget and a spending plan. Use when building a household budget, diagnosing why a household is always over, planning a major purchase, or teaching financial literacy at the household level.

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Earth systems science covering plate tectonics, landforms, erosion, biomes, hydrosphere, atmospheric circulation, and the interactions among lithosphere, hydrosphere, atmosphere, and biosphere. Provides frameworks for analyzing how physical processes shape landscapes over geological and human timescales. Use when reasoning about landforms, natural hazards, climate patterns, ocean currents, biogeography, or any question about how Earth's physical systems operate and interact.

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Human modification of Earth's systems and the geographic dimensions of environmental change. Covers climate change science (greenhouse effect, feedback loops, projections), deforestation and land use change, desertification and soil degradation, water resource management, biodiversity loss and conservation geography, pollution and environmental justice, and sustainability frameworks. Use when reasoning about human impacts on the environment, environmental policy, conservation planning, climate adaptation, or the spatial distribution of environmental risks.

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Climate physics, forcing, feedback, and attribution. Covers the greenhouse effect and radiative forcing, climate sensitivity, fast and slow feedbacks, the paleoclimate record, detection and attribution science, regional climate impacts, and the distinction between weather, climate variability, and forced climate change. Use when reasoning about global warming mechanisms, interpreting temperature or CO2 records, evaluating attribution claims for extreme events, or distinguishing signal from natural variability.

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Systems engineering covering requirements management, the V-model lifecycle, integration planning, verification and validation (V&V), interface control, trade studies, and the NASA Systems Engineering Handbook. Spans the full lifecycle from concept through operations and disposal. Includes requirements decomposition, traceability matrices, configuration management, and technical performance measures. Use when managing complex system development, writing requirements, planning integration, or conducting V&V activities.

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Theory and policy of international economic exchange. Covers comparative advantage (Ricardo, Heckscher-Ohlin), gains from trade, trade policy instruments (tariffs, quotas, subsidies), exchange rate determination, balance of payments, globalization dynamics, trade agreements, and the political economy of protectionism. Use when analyzing why countries trade, who wins and loses from trade, how exchange rates move, or the effects of trade policy interventions.

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Economics of low-income countries and the structural transformation from agrarian poverty to industrial prosperity. Covers growth models (Solow, endogenous growth, unified growth theory), the role of institutions (inclusive vs. extractive), inequality measurement and dynamics (Gini, Lorenz curve, Kuznets), poverty traps and their mechanisms (nutritional, financial, geographical), foreign aid debates, and the capability approach as an alternative development metric. Use when analyzing why some countries are rich and others poor, evaluating development interventions, or reasoning about the relationships between growth, inequality, institutions, and human well-being.

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Systematic departures from rational choice theory and their implications for economic analysis and policy. Covers cognitive heuristics (anchoring, availability, representativeness), biases (loss aversion, status quo, overconfidence), prospect theory (reference dependence, probability weighting, diminishing sensitivity), nudge theory and choice architecture, and the integration of psychological findings into economic models. Use when analyzing decision-making under uncertainty, evaluating policy interventions that exploit behavioral patterns, or assessing where standard rational-agent models break down.

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Carbon, nitrogen, phosphorus, sulfur, and water cycles — pools, fluxes, residence times, and anthropogenic perturbations. Covers the fast and slow carbon cycles, the Haber-Bosch disruption of the nitrogen cycle, the phosphorus bottleneck, the hydrological cycle, ocean acidification, and the planetary boundaries framework. Use when tracking chemical elements through atmosphere, hydrosphere, biosphere, and lithosphere; computing pool sizes and fluxes; or evaluating anthropogenic perturbations to global cycles.

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Atomic theory, periodic table organization, electron configuration, periodic trends, and isotopes/radioactivity. Covers Dalton through quantum mechanical models, electron shell filling (Aufbau, Hund, Pauli), periodic law and block structure, trend prediction (electronegativity, ionization energy, atomic radius, electron affinity), isotope notation, nuclear stability, and radioactive decay modes. Use when teaching, problem-solving, or reasoning about atomic-level chemistry.

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Deductive and inductive reasoning, formal and informal logical structure, validity, soundness, and rules of inference. Covers propositional logic, quantified reasoning, syllogisms, common inference patterns (modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism), and the distinction between deductive certainty and inductive probability. Use when the question is not whether a premise is true but whether the reasoning from premises to conclusion is logically valid.

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Structured approaches to decisions under uncertainty and complexity. Covers expected value, decision trees, multi-criteria decision analysis, System 1 vs System 2 allocation, pre-mortems, reversible vs irreversible decisions, and the distinction between good decisions and good outcomes. Use when choosing among alternatives with uncertain or multi-dimensional consequences, especially when the stakes justify a deliberate rather than intuitive process.

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Recognition and mitigation of systematic reasoning errors documented in the heuristics and biases tradition. Covers confirmation bias, availability, anchoring, representativeness, framing effects, hindsight bias, overconfidence, and motivated reasoning. Each bias is presented with its mechanism, diagnostic signal, and structured mitigation. Use when you suspect your own or another reasoner's conclusions may be shaped by systematic cognitive distortion rather than evidence.

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Systematic evaluation of arguments for structure, validity, soundness, and charitable interpretation. Covers premise identification, conclusion extraction, argument mapping, steel-manning, and the distinction between validity (form) and soundness (form plus true premises). Use when assessing an argument, reconstructing an opponent's position fairly, or preparing a rebuttal.

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Interpersonal communication theory and practice for one-on-one and small group interaction. Covers communication models (linear, transactional, constructivist), self-disclosure and Johari Window, relational dialectics, communication climate, supportive versus defensive communication, feedback models, and adapting style across relationships and contexts. Use when analyzing communication dynamics, improving relationships, giving feedback, or understanding communication breakdowns between individuals.

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Ionic, covalent, and metallic bonding, Lewis structures, VSEPR theory, molecular geometry, polarity, and intermolecular forces. Covers octet rule and exceptions, formal charge, resonance, sigma/pi bonds, orbital hybridization, electronegativity-driven bond classification, VSEPR electron-domain and molecular geometries, dipole moments, and the four intermolecular force types (London dispersion, dipole-dipole, hydrogen bonding, ion-dipole). Use when predicting molecular shapes, bond properties, or physical behavior from molecular structure.

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Stellar spectral analysis from first light to chemical abundance. Covers continuum emission and absorption, the OBAFGKM classification sequence, luminosity classes, line identification, Doppler shifts, curve-of-growth abundance analysis, and the astrophysical conclusions that follow from a spectrum. Use when classifying a star, measuring radial velocity, inferring composition or temperature, or teaching why the Sun is mostly hydrogen.

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