Last changed 2026-04-15 · stable 1d · history

First Order Theories of Individual Concepts and Propositions

Reference: John McCarthy (1979b). “First Order Theories of Individual Concepts and Propositions.” In J. E. Hayes, D. Michie, and L. I. Mikulich (eds.), Machine Intelligence 9, Ellis Horwood, pp. 129-147. (Version fetched is the revised 2000 reprint.) URL

Summary

McCarthy argues that knowledge, belief, wanting, and necessity can be formalised in ordinary sorted first-order logic — without modal operators, quotation, or possible-worlds machinery — by admitting individual concepts as first-class objects alongside the things that reify them. Where Frege had distinguished sense (the concept) from reference (the denotation), and where Carnap, Church, and Montague responded by extending logic, McCarthy responds by keeping logic ordinary and adding a domain of concepts plus a denot function mapping concepts to their denotations.

Thus Mike is the concept of Mike, mike is Mike himself, Telephone Mike is the concept of Mike’s telephone number, and telephone mike is the number. Know(Pat, Telephone Mike) is the proposition that Pat knows Mike’s telephone number; true Know(Pat, Telephone Mike) asserts it. Extensionality is expressed by explicit axioms: Know is extensional in its first (knower) argument but not its second, which is precisely why substituting equal telephone numbers inside Know fails. The paper works through knowing what vs knowing that, iterated knowledge, non-denoting concepts (Pegasus), belief, wanting, existence (via an Exists predicate that does not presuppose existence of the concept’s referent), and necessity — all in sorted FOL, with standard model theory available to study which concept-spaces satisfy which axioms.

The paper is McCarthy’s most developed statement of his reificationist, logicist methodology for mental attitudes: rather than extend the logic, extend the ontology. This is directly the substrate Elephant 2000 uses when it talks about speech acts committing agents to propositions and referring to past events and future obligations.

Key Ideas

Reify concepts as objects in sorted FOL; no modal operators, no quotation.
denot function maps concepts to their referents; extensionality becomes an axiom about particular functions rather than a global property of the logic.
Know(P, X) is extensional in P (the knower) but not in X (the knowand), explaining failure of substitutivity for knowledge.
knowing what vs knowing that are distinct; both are expressible.
Non-existent referents (Pegasus) handled by denotes(X, x) predicate rather than denot function, and by Exists/exists pair.
Concept-valued variables, functions, and constants (capitalisation convention) vs object-valued lowercase counterparts.

Connections

Ascribing Mental Qualities to Machines — the philosophical sibling paper; this gives the logical machinery for the ascriptions argued for there.
Elephant 2000 - A Programming Language Based on Speech Acts — Elephant’s program variables can range over speech acts, propositions, and commitments; the concept/object distinction here is exactly what allows a program to refer to the fact that Pat was told X rather than just to X’s value.
Knowledge Representation
Common Sense Reasoning
KIF — KIF’s individuating of propositions and sentences as first-class objects follows this lineage.
Speech Act Theory

Conceptual Contribution

Claim: Propositional attitudes and modalities can be formalised in ordinary sorted first-order logic by admitting individual concepts (and propositions) as objects with a denot mapping to their referents — no modal operators or quotation required.
Mechanism: Sorted FOL; capitalised concept-valued terms vs lowercase denotation-valued terms; denot/denotes functions and predicates; extensionality stated per-predicate via axioms like denot P1 = denot P2 => denot Know(P1,X) = denot Know(P2,X); Exists/exists to handle non-denoting concepts; true Q to lift propositions to truth values.
Concepts introduced/used: Individual Concepts, Propositional Attitudes, Extensionality, Sense and Denotation, Knowing What vs Knowing That, Reification, Sorted Logic.
Stance: foundational
Relates to: Provides the ontology on which Elephant 2000 - A Programming Language Based on Speech Acts builds its program-as-speech-act semantics; complements the ascriptive stance of Ascribing Mental Qualities to Machines; technically prefigures the object-level treatment of sentences in KIF and the commitment semantics in Agent Communication And Institutional Reality.

Backlinks

Concepts as Individuals line 7
Knowing What vs Knowing That line 6
Sorted Logic line 6
Reification line 6
Extensionality line 6
Individual Concepts line 6
Sense and Denotation line 6
index line 50
Common Business Communication Language line 23
Some Philosophical Problems from the Standpoint of Artificial Intelligence line 50
Some Philosophical Problems from the Standpoint of Artificial Intelligence line 27
Generality in Artificial Intelligence line 49
Generality in Artificial Intelligence line 30
Epistemological Problems of Artificial Intelligence line 46
Epistemological Problems of Artificial Intelligence line 27
Epistemological Problems of Artificial Intelligence line 8
Elephant 2000 - A Programming Language Based on Speech Acts line 33
Towards a Mathematical Science of Computation line 21
Programs with Common Sense line 26
Circumscription - Applications to Formalizing Common Sense Knowledge line 49
Circumscription - Applications to Formalizing Common Sense Knowledge line 28
Circumscription - Applications to Formalizing Common Sense Knowledge line 10
Circumscription - A Form of Nonmonotonic Reasoning line 34
Circumscription - A Form of Nonmonotonic Reasoning line 22
Recursive Functions of Symbolic Expressions and Their Computation by Machine line 28

Linked Pages

Agent Communication And Institutional Reality

Agent Communication and Institutional Reality

Reference: Fornara, Viganò, Colombetti (2005). Agent Communication II, LNAI 3396, Springer. Source file: 978-3-540-32258-0_1.pdf. URL

Summary

Fornara, Viganò, and Colombetti propose regarding an Agent Communication Language as a set of conventions acting on a fragment of institutional reality, defined within an artificial institution. They reformulate commitment-based ACL semantics so that all commonly used communicative act types reduce to a single basic type, declarations, within a Basic Institution that regulates the lifecycle of social commitments.

Special institutions (e.g., English Auctions) extend the Basic Institution with ontological and normative elements. The approach is notable for making the semantics of speech acts publicly verifiable and independent of agents’ mental states, while retaining a uniform formal account of institutional actions and counts-as relations.

Key Ideas

ACL messages are institutional actions governed by counts-as rules.
Basic Institution manages creation/update/cancellation of social commitments.
All speech act types reducible to declarations within the institution.
Special institutions layer domain norms and ontologies on top.
English Auction given as worked example.

Connections

Conceptual Contribution

Claim: An ACL is best understood as a set of conventions operating on institutional reality; all communicative act types reduce to declarations within a Basic Institution that governs the lifecycle of social commitments.
Mechanism: Defines artificial institutions with counts-as rules; models message effects as declarations creating/updating/cancelling commitments; layers domain norms in Special Institutions (English Auction worked example).
Concepts introduced/used: Commitment-based Semantics, Institutional Reality, Counts-as Rules, Declarations, Performatives, Speech Act Theory, Public Semantics, Verifiable Semantics, Mentalistic Semantics, Ontologies, FIPA-ACL, Multi-Agent Systems
Stance: formal-semantic
Relates to: Offers the publicly-verifiable alternative to mental-state semantics of FIPA-ACL, which A Common Ontology Of ACLs then unifies via roles; grounded philosophically in Foundations Of Illocutionary Logic.

Knowledge Interchange Format

First-order-logic-based language (Genesereth) used as a neutral content language for KQML and Ontolingua.

In this vault

Ascribing Mental Qualities to Machines

Reference: John McCarthy (1979). Stanford CS Department; reprinted in Formalizing Common Sense: Papers by John McCarthy (V. Lifschitz ed., Ablex, 1990). Source file: mccarthy-ascribing.pdf. URL

Summary

McCarthy argues that ascribing beliefs, desires, intentions, knowledge, and other mental qualities to machines (including simple ones like thermostats) is legitimate when the ascription conveys the same information about the machine that it would about a person, and useful when it helps us predict, repair, or improve the machine’s behaviour. He proposes two new definitional tools — definitions relative to an approximate theory, and second-order structural definitions — so that mental-state vocabulary can be applied to physical systems conservatively rather than by reduction to physics.

This is the philosophical foundation for the entire mentalistic (BDI) tradition in agent research that ACL Rethinking Principles pushes back against. Singh cites McCarthy as the origin of the view that agent communication can be specified by ascribing beliefs and intentions; McCarthy himself is already careful to warn that such ascriptions must be conservative and may be merely convenient shorthand for structural facts.

Key Ideas

Ascribing mental qualities is warranted when it expresses information about the machine concisely — not because the machine “really” has a mind.
Ascription is most useful precisely when the structure of the system is incompletely known; for fully-listed programs one could in principle simulate instead.
Mental qualities should be ascribed separately (belief without desire, desire without consciousness, etc.) rather than bundled into a monolithic concept of mind; different machines warrant different subsets.
Novel definitional tools: (1) definitions relative to an approximate theory — a mental predicate is defined only within a coarser theory that abstracts away from physical detail; (2) second-order structural definitions — mental qualities defined by the existence of certain structural roles in the system.
Epistemological vs metaphysical adequacy of representations: AI needs representations that capture what is knowable about a situation, not just what is ultimately true.
The approach is intended as conservative (liberal in what it admits having some mental qualities, strict in how each is attributed).

Connections

Conceptual Contribution

Claim: It is legitimate and often necessary to ascribe mental qualities (belief, desire, intention, knowledge) to machines, provided the ascription is conservative, quality-by-quality, and grounded either in an approximate theory that abstracts away from physical detail or in a second-order structural definition that names the role the quality plays.
Mechanism: Philosophical / definitional. Distinguishes epistemological from metaphysical adequacy of representations, separates mental qualities rather than bundling them, and introduces approximate-theory and structural-definition techniques for defining predicates like believes(M, P) over machines.
Concepts introduced/used: Intentional Stance, Mentalistic Semantics, Approximate Theory, Structural Definitions, Epistemological Adequacy, Common Sense Reasoning
Stance: foundational / philosophical
Relates to: Source of the mental-ascription tradition that Intention Is Choice with Commitment formalises and that Semantics and Conversations for an ACL applies to KQML. ACL Rethinking Principles argues this tradition overreaches when used as a compliance criterion for ACLs; McCarthy’s own hedges about conservativism actually support that pushback.

Elephant 2000: A Programming Language Based on Speech Acts

Reference: John McCarthy (1989, revised). Formal Reasoning Group, Stanford University. Source file: elephant.pdf. URL

“I meant what I said, and I said what I meant. / An elephant’s faithful, one hundred percent! / moreover, / An elephant never forgets!”

Summary

McCarthy proposes Elephant 2000, a speculative programming language whose inputs and outputs are speech acts — requests, questions, offers, acceptances, declinations, permissions, and promises — rather than ordinary I/O. A program’s correctness is then partly defined by the “happy performance” of those acts in Austin’s sense: answers must be truthful and responsive, promises must be kept, and the program must not accept what it has no authority to accept. The paper is an essay of seven design theses, most strikingly:

An Elephant program is itself a logical sentence (or syntactic sugar for one); its extensional correctness properties follow by logical consequence without a separate theory of programming à la Hoare.
Elephant programs do not need data structures: they can refer directly to the past (history of events and states), just as natural-language speakers do (“the passenger has a reservation iff she made one and hasn’t cancelled it”).
Programs have both input-output specifications (generalising illocutionary speech acts) and accomplishment specifications (generalising perlocutionary acts — what the program actually brings about in the world).
Commercial transactions exchange obligations; an Elephant program’s specification may include the fact that the obligation exchange happens as intended, again as a logical sentence.

McCarthy explicitly departs from Searle/Austin by taking a design stance (Dennett) on speech acts, introducing abstract performatives (including purely internal commitments the agent makes to itself) as a category of program event. The paper is the direct programming-language-side ancestor of modern Agent Communication Languages, Commitment-based Semantics, and Intent Formalization — all written a decade before the ACL field got going.

Key Ideas

Speech-act I-O language: programs communicate via request, question, offer, accept, decline, permission, promise, assertion, plus internal commitment
Program-as-logical-sentence: extensional properties are logical consequences, no Hoare axioms required
Direct reference to the past: no data structures, just history queries (has-reservation(psgr, flt) ≡ made-reservation ∧ ¬cancelled)
Illocutionary vs. perlocutionary specs: input-output (program’s own behaviour) vs. accomplishment (effects in the world)
Abstract performatives — internal commitments whose content is independent of outward expression
Obligation exchange as a first-class specification element for commercial/institutional programs
Takes a design stance on speech acts — adapts Austin/Searle rather than inheriting them
Authority / permission / obligation are specification concerns: the program need not be conscious of them
Explicit claim: deliberately non-AI — Elephant usages that do not require intelligence are the focus

Connections

Ascribing Mental Qualities to Machines — McCarthy’s prior paper on when it’s useful to ascribe beliefs/intentions to programs
Common Business Communication Language — McCarthy 1982, explicitly cited as the motivating application
Towards a Mathematical Science of Computation — McCarthy 1963; originates the program-as-logical-object agenda Elephant radicalises.
Correctness of a Compiler for Arithmetic Expressions — McCarthy & Painter 1967; first proof-of-concept for the verification programme Elephant extends to speech-act semantics.
First Order Theories of Individual Concepts and Propositions — McCarthy 1979; the logical machinery for propositional attitudes that Elephant’s commitments and history-referring constructs presuppose.
Circumscription - A Form of Nonmonotonic Reasoning — McCarthy 1986; the defeasibility substrate for commitment revision.
The Knowledge Level — Newell 1982; Elephant is a programming language whose native level of description is Newell’s knowledge level.
Foundations Of Illocutionary Logic — Searle & Vanderveken, the philosophical spine McCarthy adapts
Speech Act Theory
Agent Communication Languages
KQML
KQML Overview
KQML as an Agent Communication Language
FIPA-ACL
Performatives
Commitment-based Semantics
Agent Communication And Institutional Reality
Agent-Oriented Programming
Intention Is Choice with Commitment
Assigning Meanings to Programs
Hoare Logic
Formal Verification
Verifiable Semantics
Foundations of Logic Programming - Lloyd
Intent Formalization - A Grand Challenge for Reliable Coding
A Scalable Communication Protocol for Networks of LLMs
Institutional Reality

Sorted Logic

First-order logic with typed variables — used to keep individual concepts, their denotations, and propositions cleanly separated.

In this vault

First Order Theories of Individual Concepts and Propositions

Reification

Turning a predicate, function, or modality into a first-order object so it can be quantified over and reasoned about explicitly. McCarthy’s technique for attitudes.

In this vault

First Order Theories of Individual Concepts and Propositions

Knowing What vs Knowing That

Knowledge of a referent (knowing what X is) versus knowledge of a proposition (knowing that p); logically distinguished via individual-concept machinery.

In this vault

Sense and Denotation

Frege: every meaningful expression has both a sense (mode of presentation) and a denotation (referent). McCarthy formalises the sense/denotation distinction inside first-order logic rather than leaving it modal.

In this vault

Extensionality

Principle that a predicate’s meaning is its extension (set of satisfying tuples); fails for propositional-attitude contexts, motivating McCarthy’s first-order theory of individual concepts.

In this vault

First Order Theories of Individual Concepts and Propositions

Propositional Attitudes

Mental states such as believing, desiring, or intending that take propositions as their content. ACL semantics have traditionally been specified in terms of sender and recipient propositional attitudes.

In this vault

Individual Concepts

McCarthy-Church: the sense of a name — the concept of an individual distinct from the individual itself — needed for sentences about belief, knowledge, and identity across modal contexts.

In this vault

Speech Act Theory

Philosophy-of-language framework (Austin, Searle, Vanderveken) in which utterances perform actions (illocutionary acts) — the semantic backbone of most Agent Communication Languages.

Sources

Foundations Of Illocutionary Logic — Searle & Vanderveken
Three Models for the Description of Language — Chomsky, foundations
Agent Communication And Institutional Reality

Applied in

Lineage

graph TD
  A["Austin (1962)<br/>How to Do Things with Words"] --> A1[Locutionary]
  A --> A2[Illocutionary]
  A --> A3[Perlocutionary]
  A2 --> S["Searle (1969, 1975)<br/>Speech Acts · Taxonomy of Illocutionary Acts"]
  S --> S1[Assertives]
  S --> S2[Directives]
  S --> S3[Commissives]
  S --> S4[Expressives]
  S --> S5[Declarations]
  G["Grice (1975)<br/>Logic and Conversation"] -.cooperative principle.-> S
  S --> V["Searle & Vanderveken (1985)<br/>Foundations of Illocutionary Logic"]
  V --> M["McCarthy (1989)<br/>Elephant 2000"]
  V --> KQML[KQML performatives]
  V --> FIPA[FIPA-ACL performatives]
  M --> FIPA
  KQML --> ACL[[Agent Communication Languages]]
  FIPA --> ACL

Papers: How to Do Things with Words · Speech Acts - An Essay in the Philosophy of Language · A Taxonomy of Illocutionary Acts · Logic and Conversation · Foundations Of Illocutionary Logic · Elephant 2000 - A Programming Language Based on Speech Acts

Common Sense Reasoning

Reasoning about everyday physical and social situations using informal but robust inferences — the enduring grand challenge McCarthy posed for AI.

In this vault

Knowledge Representation

The discipline of encoding knowledge about a domain in a machine-usable form (logic, frames, semantic nets, ontologies) so agents can reason over it.

First Order Theories of Individual Concepts and Propositions

Summary

Key Ideas

Connections

Conceptual Contribution

Tags

Backlinks