Updates and counterfactuals
Abstract
We study the problem of combining updates—a special instance of theory change—and counterfactual conditionals in propositional knowledge bases. Intuitively, an update means that the world described by the knowledge base has changed. This is opposed to revisions—anotherinstance of theory change—where our knowledge about a static world changes. A countcrfactual implication is a statement of the form ‘If A were the case, then B would also be the case’, where the negation of A may be derivable from our current knowledge. We present a decidable logic, called VCU2, that has both update and counterfactual implication as connectives in the object language. Our update operator is a generalization of operators previously proposed and studied in the literature. We show that our operator satisfies certain postulates set forth for any reasonable update. The logic VCU2 is an extension of D. K. Lewis' logic VCU for counterfactual conditionals. The semantics of VCU2 is that of a multimodal prepositional calculus, and is based on possible worlds. The infamous Ramsey Rule becomes a derivation rule in our sound and complete axiomatization. We then show that Gärdenfors' Triviality Theorem, about the impossibility to combine theory change and counterfactual conditionals via the Ramsey Rule, does not hold in our logic. It is thus seen that the Triviality Theorem applies only to revision operators, not to updates.
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Findings on explanation accumulated in humanities and social sciences show that explanation is intrinsically contrastive.
“Findings on explanation accumulated in humanities and social sciences show that it is intrinsically contrastive [11].”
From A Survey of Contrastive and Counterfactual Explanation Generation Methods for Explainable Artificial Intelligence (2021) · cites this paper as [11]
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Stepin, I., Alonso, J. M., Catala, A., & Pereira-Farina, M. (2021) · IEEE Access · doi:10.1109/access.2021.3051315 · Cited by 376 · see citing works
On the complexity of propositional knowledge base revision, updates, and counterfactuals
Eiter, T., & Gottlob, G. (1992) · Artificial Intelligence · doi:10.1016/0004-3702(92)90018-s · Cited by 351 · see citing works
An overview of transaction logic
Bonner, A. J., & Kifer, M. (1994) · Theoretical Computer Science · doi:10.1016/0304-3975(94)90190-2 · Cited by 145 · see citing works
“Subsequently, though, Grahne and Mendelzon proved that updating sets of ground atoms with arbitrary propositional formulas can be done in polynomial time.”
BackgroundInfluentialPropositional belief base update and minimal change
Herzig, A., & Rifi, O. (1999) · Artificial Intelligence · doi:10.1016/s0004-3702(99)00072-7 · Cited by 140 · see citing works
“The classical explanation as given in [18] is as follows.”
BackgroundMakinson, D. (1993) · Studia Logica · doi:10.1007/bf01057652 · Cited by 129 · see citing works
A PROBABILISTIC SEMANTICS FOR COUNTERFACTUALS. PART A
Leitgeb, H. (2011) · The Review of Symbolic Logic · doi:10.1017/s1755020311000153 · Cited by 96 · see citing works
Unifying default reasoning and belief revision in a modal framework
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On specifying database updates
Reiter, R. (1995) · The Journal of Logic Programming · doi:10.1016/0743-1066(95)00049-p · Cited by 77 · see citing works
“A wide variety of proposals for this exist in the literature (e.g., Abiteboul [1]; Grahne [13]; Katsuno and Mendelzon [20]; Winslett [48]; Fagin, Ullman, and Vardi [10]; Ginsberg and Smith [12]; Guessoum and Lloyd [16] [17]; Manchanda and Warren [32]; Kowalski [22]; Bonner and Kifer [6]).”
BackgroundMethodInfluentialDynamic doxastic logic: why, how, and where to?
Leitgeb, H., & Segerberg, K. (2007) · Synthese · doi:10.1007/s11229-006-9143-8 · Cited by 67 · see citing works
“Proofs of these results, which generalize those of Grahne (1991), are given in Segerberg (2005, unpublished manuscript).”
BackgroundResultA Unified View of Consequence Relation, Belief Revision, and Conditional Logic *
Katsuno, H., & Satoh, K. (1995) · doi:10.1093/oso/9780198538615.003.0003 · Cited by 66 · see citing works
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“Numerous results have been established that reveal profound connections between Belief Revision and areas like Nonmonotonic Reasoning [10, 33, 61, 63, 106], Reasoning about Action [8, 16, 36, 44, 46, 72–74, 77, 92, 109], Conditionals [26, 30, 35, 37, 59, 88, 82] and Possibility Theory [20, 21, 4].”
A sequent calculus and a theorem prover for standard conditional logics
Olivetti, N., Pozzato, G. L., & Schwind, C. B. (2007) · ACM Transactions on Computational Logic · doi:10.1145/1276920.1276924 · Cited by 59 · see citing works
FROM CAUSAL MODELS TO COUNTERFACTUAL STRUCTURES
Halpern, J. Y. (2012) · The Review of Symbolic Logic · doi:10.1017/s1755020312000305 · Cited by 55 · see citing works
“Axioms: There are a number of well-known sound and complete axiomatizations for counterfactual logic (see, e.g., [Burgess 1981; Bell 1989; Chellas 1980; Grahne 1991; Katsuno and Satoh 1991; Lewis 1971; Lewis 1973; Lewis 1974]).”
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Chou, T. S. C., & Winslett, M. (1994) · Journal of Automated Reasoning · doi:10.1007/bf00881886 · Cited by 47 · see citing works
“> (pr-stats 12) [12] COT DAwr ZEEO) (ER DTET ZEEO) (ST AgT ZERO) (TOM FAUCET) (LOC FAUCET) (LT TgT TBOIL) (LIQUID-FLOg) T r a n s i t i o n ( s ) : To [15] by (MOVE TO STOVE) To [16] by (MOVE TO TABLE) To [14] by (TURJ OI STOVE) To [17] by (TUEW OFF FAUCET) > (pr-state 17) [17] (EQ DAgT ZEZ0) (EQ DT~r ZEZ0) (OT AgT ZE…”
BackgroundMethodOn the complexity of propositional knowledge base revision, updates, and counterfactuals
Eiter, T., & Gottlob, G. (1992) · ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS) · doi:10.1145/137097.137886 · Cited by 45 · see citing works
“Furthermore, it was not clear under which restrictions the single methods would become tractable.”
BackgroundCoherence and Conservatism in the Dynamics of Belief
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Counterfactuals and Updates as Inverse Modalities
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“It turns out that the theory of updates proposed by Katsuno and Mendelzon [10] is compatible with the Ramsey Rule [6].”
ResultInfluentialTwo notions of epistemic validity
Costa, H. A., & Levi, I. (1996) · Synthese · doi:10.1007/bf00413768 · Cited by 39 · see citing works
“/(see (Lewis 1973)) in (Grahne 1991) and to R Giirdenfors' model ofl?C offered in (G~irdenfors 1978).”
MethodReasoning About Merged Information
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“We think however that correspondence with the other semantic systems can be shown along the same lines as by Grahne [16].”
On formalizing database updates: Preliminary report
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ALX, an action logic for agents with bounded rationality
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The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions
Eiter, T., & Gottlob, G. (1996) · Journal of Computer and System Sciences · doi:10.1006/jcss.1996.0083 · Cited by 29 · see citing works
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Bonatti, P. A., & Eiter, T. (1996) · Theoretical Computer Science · doi:10.1016/0304-3975(95)00192-1 · Cited by 28 · see citing works
Weak AGM postulates and strong Ramsey Test: A logical formalization
Giordano, L., Gliozzi, V., & Olivetti, N. (2005) · Artificial Intelligence · doi:10.1016/j.artint.2005.06.004 · Cited by 25 · see citing works
“To this group belong the proposals by Grahne [13], and Ryan and Schobbens [32].”
BackgroundMethodInfluentialConditional logics of belief change
Friedman, N., & Halpern, J. Y. (1994) · Cited by 25 · see citing works
Iterated Belief Revision and Conditional Logic
Giordano, L., Gliozzi, V., & Olivetti, N. (2002) · Studia Logica · doi:10.1023/a:1014602224874 · Cited by 22 · see citing works
Can Bayes' Rule be Justified by Cognitive Rationality Principles?
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Tableau calculus for preference-based conditional logics
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Herzig, A. (1998) · Springer eBooks · doi:10.1007/978-94-011-5054-5_5 · Cited by 20 · see citing works
Beliefs in conditionals vs. conditional beliefs
Leitgeb, H. (2007) · Topoi · doi:10.1007/s11245-006-9003-7 · Cited by 20 · see citing works
The PMA and relativizing change for action update
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Standard Sequent Calculi for Lewis’ Logics of Counterfactuals
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“Independently from counterfactuals, conditional logics have found an interest in several fields of knowledge representation; for instance, they have been used to model belief change [10].”
A logic for revision and subjunctive queries
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Tableau Calculi for Preference-Based Conditional Logics
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“1 These axioms corresponds to Uniformity Propertyin [10, 16].”
BackgroundMethodInfluentialGrahne, G., Mendelzon, A. O., & Revesz, P. Z. (1992) · ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS) · doi:10.1145/137097.137882 · Cited by 19 · see citing works
Self-citationNested Sequent Calculi for Conditional Logics
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“They have been used to reason about prototy pical properties [10] and to model belief change [14, 12].”
MethodReapproaching Ramsey: Conditionals and Iterated Belief Change in the Spirit of AGM
Rott, H. (2011) · Journal of Philosophical Logic · doi:10.1007/s10992-011-9177-3 · Cited by 15 · see citing works
“Members of this party include Ryan and Schobbens [40], Grahne [15] and Crocco and Herzig [9].”
BackgroundA Standard Internal Calculus for Lewis’ Counterfactual Logics
Olivetti, N., & Pozzato, G. L. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-24312-2_19 · Cited by 14 · see citing works
“In the recent history of conditional logics the work by Lewis [15] has a prominent place (among others [5,18,12,10]).”
BackgroundOn the Ramsey Test without Triviality
Leitgeb, H. (2010) · Notre Dame Journal of Formal Logic · doi:10.1215/00294527-2010-003 · Cited by 14 · see citing works
“where ⋆ is the so-called belief update operator of Grahne (1991) and”
Theorem proving for conditional logics: CondLean and GOALDUCK
Olivetti, N., & Pozzato, G. L. (2008) · Journal of Applied Non-Classical Logics · doi:10.3166/jancl.18.427-473 · Cited by 13 · see citing works
“…(Delgrande, 1987; Kraus et al. , 1990; Crocco et al. , 1992; Friedman et al. , 2001; Giordano et al. , 2005b), deductive databases (Gabbay et al. , 2000a), belief revision (Grahne, 1998; Giordano et al. , 2005a; Giordano et al. , 2002) and natural language semantics (Costello et al. , 1999).”
BackgroundA Conditional Logic for Belief Revision
Giordano, L., Gliozzi, V., & Olivetti, N. (1998) · Lecture notes in computer science · doi:10.1007/3-540-49545-2_20 · Cited by 13 · see citing works
Conditionals and the Ramsey Test
Lindström, S., & Rabinowicz, W. (1998) · Springer eBooks · doi:10.1007/978-94-011-5054-5_4 · Cited by 13 · see citing works
Updates and Subjunctive Queries
Grahne, G., & Mendelzon, A. O. (1995) · Information and Computation · doi:10.1006/inco.1995.1017 · Cited by 13 · see citing works
Self-citationSano, K. (2009) · Journal of Logic Language and Information · doi:10.1007/s10849-009-9090-0 · Cited by 12 · see citing works
A Conditional Logic-Based Argumentation Framework
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“areas [9] like belief revision [16], data base and knowledge update [19] natural language semantics for handling hypothetical and counterfactual sentences [23], non-monotonic and prototypical reasonings [11, 20], causal inference [17] and logic programming [14], just to mention some seminal works.”
BackgroundRevision, Acceptability and Context
Gabbay, D. M., Rodrigues, O., & Russo, A. (2010) · Cognitive technologies · doi:10.1007/978-3-642-14159-1 · Cited by 12 · see citing works
On the semantics of belief revision systems
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Self-citationVINTE: An Implementation of Internal Calculi for Lewis’ Logics of Counterfactual Reasoning
Girlando, M., Lellmann, B., Olivetti, N., et al. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-66902-1_9 · Cited by 10 · see citing works
“Just to mention a few (see [1] for a complete bibliography), they have been used to reason about prototypical properties, to model belief change [8], to reason about access control policies [5], to formalize epistemic change in a multi-agent setting [2,4].”
BackgroundConditional and Preferential Logics: Proof Methods and Theorem Proving
Pozzato, G. L. (2010) · Cited by 10 · see citing works
A Calculus and Complexity Bound for Minimal Conditional Logic
Olivetti, N., & Schwind, C. B. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45446-2_25 · Cited by 8 · see citing works
“For instance, in knowledge representation, conditional logics have been used to represent and reason about prototypical properties [14], the have been used to model knowledge and database update [18], belief revision [1,15,16].”
Hypersequent Calculi for Lewis’ Conditional Logics with Uniformity and Reflexivity
Girlando, M., Lellmann, B., Olivetti, N., et al. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-66902-1_8 · Cited by 8 · see citing works
“A successful attempt to relate conditional logic and belief update (as opposite to belief revision) was carried out by Grahne [8], who established a precise mapping between belief update operators and Lewis’ logic VCU.”
BackgroundCounterfactuals and Updates as Inverse Modalities
Ryan, M. D., Schobbens, P., & Rodrigues, O. (1996) · Cited by 8 · see citing works
Uniform Labelled Calculi for Conditional and Counterfactual Logics
Girlando, M., Negri, S., & Sbardolini, G. (2019) · Lecture notes in computer science · doi:10.1007/978-3-662-59533-6_16 · Cited by 8 · see citing works
Verification of Inconsistency-Aware Knowledge and Action Bases
Calvanese, D., Kharlamov, E., Montali, M., et al. (2013) · Oxford University Research Archive (ORA) (University of Oxford) · Cited by 7 · see citing works
Nested sequent calculi and theorem proving for normal conditional logics: The theorem prover NESCOND
Olivetti, N., & Pozzato, G. L. (2015) · Intelligenza Artificiale · doi:10.3233/ia-150082 · Cited by 7 · see citing works
“Itturnsoutthatallformsofinference studied in [26] are particular cases of well-known logics); – to model database update [18, 22] and belief a conditional logic, more precisely a variant of the logic introduced in [27], to formalize knowledge-update as defined by Katsuno and Mendelzon in [25]; in…”
Querying disjunctive databases through nonmonotonic logics
Bonatti, P. A., & Eiter, T. (1995) · Lecture notes in computer science · doi:10.1007/3-540-58907-4_7 · Cited by 7 · see citing works
Belief Revision, Diagnosis and Repair
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Conditional Logics for Defeasible Reasoning
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Drawing Inferences from Conditionals
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Self-citationVerification of generalized inconsistency-aware knowledge and action bases
Calvanese, D., Montali, M., & Santoso, A. (2015) · Open Research (University of Surrey) · Cited by 5 · see citing works
Conditioning by Minimizing Accessibility
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“Although the relation between conditionals and the operators of update and revision is straightforward when the conditionals are not nested, there are results that extend this link to full conditional logics (see [14,16] for update, and [3,10,11] for revision).”
BackgroundResultMetaprogramming through intensional deduction: Some examples
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A reason maintenance perspective on relevant Ramsey conditionals
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BackgroundMethodInfluentialAsking about possibilities — Revision and update semantics for subjunctive queries Extended report
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Nested sequent calculi for normal conditional logics
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“They have been used to reason about prototypical properties [16] and to model belief change [21, 18].”
Counterfactual Reasoning via Grounded Distance
Aguilera-Ventura, C., Herzig, A., Liu, X., et al. (2023) · doi:10.24963/kr.2023/1 · Cited by 4 · see citing works
“AGM (belief revision) (Grove 1988), KM (belief update) (Grahne 1998), and KLM (preferential reasoning) (Kraus, Lehmann, and Magidor 1990).”
BackgroundCalculi, countermodel generation and theorem prover for strong logics of counterfactual reasoning
Girlando, M., Lellmann, B., Olivetti, N., et al. (2021) · Journal of Logic and Computation · doi:10.1093/logcom/exab084 · Cited by 4 · see citing works
Belief Revision and the Ramsey Test: A Solution
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“Grahne [10] has proposed a conditional logic which combines updates and counterfactuals and which does not entail triviality.”
BackgroundPreferential Semantics for the Logic of Comparative Similarity over Triangular and Metric Models
Alenda, R., & Olivetti, N. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-33353-8_1 · Cited by 4 · see citing works
“From the axiomatic point of view, we show below an axiomatization of VCU [9, 10, 11] (in addition to axioms and rules of classical propositional calculus):”
BackgroundInfluentialNormative, subjunctive and autoepistemic defaults
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Model Update for System Modifications
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Strategies for Belief Revision
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All Other Things Being Equal: On a Notion of Inertia in Conditional Logic
del Cerro, L. F., & Herzig, A. (1997) · Trends in logic · doi:10.1007/978-94-011-5524-3_7 · Cited by 2 · see citing works
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BELIEF-REVISION, THE RAMSEY TEST, MONOTONICITY, AND THE SO-CALLED IMPOSSIBILITY RESULTS
Tennant, N. W. (2008) · The Review of Symbolic Logic · doi:10.1017/s1755020308090023 · Cited by 1 · see citing works
“See Katsuno & Mendelzon (1991) and Grahne (1991). The expression ‘supposed to’ is used here to indicate that the present author would be critical of update-theorists’ conception of what is being reevaluated when registering changes in the world (as opposed to changes in our knowledge of it).”
BackgroundMonotonicity in Intuitionistic Minimal Change Semantics Given Gärdenfors’ Triviality Result
Liu, X. (2020) · Lecture notes in computer science · doi:10.1007/978-3-662-62843-0_6 · Cited by 1 · see citing works
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Prediction of Traffic Participant Behavior in Driving Environment Based on Counterfactual Inference
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A Kripke-Lewis semantics for belief update and belief revision
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The Logic of AGM Learning from Partial Observations
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Imagination and Suppositional Thought
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Automated Reasoning for Conditional Logics: the Theorem Prover Condlean 3.1
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Verification of Inconsistency-Aware Knowledge and Action Bases (Extended Version)Preprint
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Contributions aux approches logiques de l'argumentation en intelligence artificielle
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Tableaux for Reasoning about Atomic Updates
Fermüller, C. G., Moser, G., & Zach, R. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45653-8_44
ãukaszewicz, W., & Madalińska-Bugaj, E. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45517-5_8
“Knowledge base update (KBU for short) [14, 15, 11, 9, 3, 10] is similar to KBR with the exception that KB represents dynamic world and represents the e ect of an action to be performed.”
Background
- Authors
- Grahne, G.
- Affiliations
- University of Helsinki (FI)
- Corresponding author
- Grahne, G
- Venue
- Journal of Logic and Computation
- Publisher
- Oxford University Press (OUP)
- Published
- 1998-02-01
- Volume
- 8
- Issue
- 1
- Pages
- 87-117
- ISSN
- 0955-792X (ISSN-L)
- 1465-363X
- OpenAlex
- W3436040
- Cited by
- 123
- References
- 0
- Citations by year
- 2026: 1 · 2024: 3 · 2023: 3 · 2022: 11 · 2021: 3 · 2020: 3 · 2019: 2 · 2017: 3 · 2016: 2 · 2015: 4 · 2013: 8 · 2012: 4
- FWCI
- 5.72
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Logic and Computation (publishedVersion)
- Principles of Knowledge Representation and Reasoning
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Algebra and Logic
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Keywords
- knowledge base updating, counterfactuals, theory change, knowledge base revision, Kripke semantics, Ramsey test, axiomatization
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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