arXiv subjects

Fausto Barbero

Publications and source records attributed to Fausto Barbero.

16 recordsLinked to original sources

arXiv2026

Labelled Sequent Calculi for Propositional Team Logics

Team semantics is a general framework where formulas are not interpreted with respect to a single point of evaluation, but with respect to sets of such points. Team semantics is used in dependence logic, to reason about dependencies between variables, and in inquisitive logic, to formalize the meaning of questions. We provide sound and complete labelled sequent calculi for four logics based on team semantics: basic inquisitive logic, propositional intuitionistic dependence logic, and their respective extensions with tensor disjunction. For technical reasons, we restrict ourselves to languages with finitely many propositional atoms. The rules of weakening, contraction and cut are shown to be admissible in each of our calculi. In the last part of the paper, we present terminating proof search procedures for variants of our proof systems, in which labels have a simplified structure.

cs.LO↗

arXiv2026

Possible and impossible conditionals for team logics

We study whether a logic based on team semantics can be enriched with a conditional satisfying minimal requirements, such as preservation of the closure property of the logic, Modus Ponens, and the Deduction Theorem. We show that such well-behaved conditionals exist for downward or upward closed logics, but do not typically exist for union closed, convex or intersection closed logics. We also briefly investigate conditionals satisfying weaker requirements.

math.LO↗

arXiv2024

Two strong undefinability results in inquisitive and team semantics

We prove two (strong) undefinability results for logics based on inquisitive semantics (or its variant, team semantics). Namely: 1) we show the undefinability of intuitionistic implication in extended propositional inquisitive logic with tensor; 2) we show the undefinability of global disjunction in extended propositional dependence logic.

math.LO↗

arXiv2023

Axiomatizations of causal reasoning under indeterministic causal laws

We investigate the generalization of causal models to the case of indeterministic causal laws that was suggested in Halpern (2000). We give an overview of what differences in modeling are enforced by this more general perspective, and propose an implementation of generalized models in the style of the causal team semantics of Barbero & Sandu (2020). In these models, the laws are not represented by functions (as in the deterministic case), but more generally by relations. We point out significant differences in the indeterministic vs. the deterministic case, both for what concerns the axiomatization of counterfactuals and the definability of causal notions in terms of them. We notice, for instance, that the notions of parenthood and direct cause, differently from the deterministic case, come apart. We provide two main strongly complete axiomatizations, one for the class of indeterministic causal models and one for their team generalizations, which can also represent uncertainty about the state of the system. Then, we also identify axioms that allow specializing the axiomatizations to a number of significant subclasses, characterized by properties such as acyclicity, totality and determinism of the causal laws. We also see that a minor change in the notion of signature of the models has a dramatic impact; in particular, it makes so that the deterministic subclass of models become undefinable in the usual Halpern-style counterfactual language. We see that the definability of determinism can be recovered either by a restriction of the class of models, by allowing right-nested counterfactuals, or by introducing an operator for information update.

cs.LO↗

arXiv2023

Multiteam semantics for interventionist counterfactuals: probabilities and causation

In [4], we introduced an extension of team semantics (causal teams) which assigns an interpretation to interventionist counterfactuals and causal notions based on them (as e.g. in Pearl's and Woodward's manipulationist approaches to causation). We now present a further extension of this framework (causal multiteams) which allows us to talk about probabilistic causal statements. We analyze the expressivity resources of two causal-probabilistic languages, one finitary and one infinitary. We show that many causal-probabilistic notions from the field of causal inference can be expressed already in the finitary language, and we prove a normal form theorem that throws new light on Pearl's ``ladder of causation''. On the other hand, we provide an exact semantic characterization of the infinitary language, which shows that this language captures precisely those causal-probabilistic statements that do not commit us to any specific interpretation of probability; and we prove that no usual, countable language is apt for this task.

cs.LO↗

arXiv2023

Strongly complete axiomatization for a logic with probabilistic interventionist counterfactuals

Causal multiteam semantics is a framework where probabilistic notions and causal inference can be studied in a unified setting. We study a logic (PCO) that features marginal probabilities and interventionist counterfactuals, and allows expressing conditional probability statements, do expressions and other mixtures of causal and probabilistic reasoning. Our main contribution is a strongly complete infinitary axiomatisation for PCO.

cs.LO↗

arXiv2023

Expressivity Landscape for Logics with Probabilistic Interventionist Counterfactuals

Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be formalized together and studied logically. We discover complete characterizations of expressivity for several logics that can express probabilistic statements, conditioning and interventionist counterfactuals. The results characterize the languages in terms of families of linear inequalities and closure conditions that define the corresponding classes of causal multiteams; we find that the strict tensor disjunction, an operator typical of team semantics but absent from the literature on causation, is needed to capture the full class of all linear inequalities. The characterizations yield a strict hierarchy of expressive power and some undefinability results.

cs.LO↗

arXiv2022

Characterizing counterfactuals and dependencies over causal and generalized causal teams

We analyze the causal-observational languages that were introduced in Barbero and Sandu (2018), which allow discussing interventionist counterfactuals and functional dependencies in a unified framework. In particular, we systematically investigate the expressive power of these languages in causal team semantics, and we provide complete natural deduction calculi for each language. Furthermore, we introduce a generalized semantics which allows representing uncertainty about the causal laws, and analyze the expressive power and proof theory of the causal-observational languages over this enriched semantics.

math.LO↗

arXiv2021

Observing Interventions: A logic for thinking about experiments

This paper makes a first step towards a logic of learning from experiments. For this, we investigate formal frameworks for modeling the interaction of causal and (qualitative) epistemic reasoning. Crucial for our approach is the idea that the notion of an intervention can be used as a formal expression of a (real or hypothetical) experiment. In a first step we extend the well-known causal models with a simple Hintikka-style representation of the epistemic state of an agent. In the resulting setting, one can talk not only about the knowledge of an agent about the values of variables and how interventions affect them, but also about knowledge update. The resulting logic can model reasoning about thought experiments. However, it is unable to account for learning from experiments, which is clearly brought out by the fact that it validates the no learning principle for interventions. Therefore, in a second step, we implement a more complex notion of knowledge that allows an agent to observe (measure) certain variables when an experiment is carried out. This extended system does allow for learning from experiments. For all the proposed logical systems, we provide a sound and complete axiomatization.

cs.AI↗

arXiv2020

Thinking About Causation: A Causal Language with Epistemic Operators

This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the side of the object language, we add operators to express knowledge and the act of observing new information. We provide a sound and complete axiomatization of the logic, and discuss the relation of this framework to causal team semantics.

cs.AI↗

arXiv2020

Counterfactuals and dependencies on causal teams: expressive power and deduction systems

We analyze the causal-observational languages that were introduced in Barbero and Sandu (2018), which allow discussing interventionist counterfactuals and functional dependencies in a unified framework. In particular, we systematically investigate the expressive power of these languages in causal team semantics, and we provide complete natural deduction calculi for each language. As an intermediate step towards the completeness, we axiomatize the languages over a generalized version of causal team semantics, which turns out to be interesting also in its own right.

math.LO↗

arXiv2019

Complexity of syntactical tree fragments of Independence-Friendly logic

A dichotomy result of Sevenster (2014) completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain "Henkin" or "signalling" patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to be essentially first-order. In the present paper we develop the machinery which is needed in order to extend the results of Sevenster to non-prenex, regular IF sentences. This involves shifting attention from quantifier prefixes to a (rather general) class of syntactical tree prefixes. We partially classify the fragments of regular IF logic that are thus determined by syntactical trees; in particular, a) we identify three tree prefixes that are neither signalling nor Henkin, and yet express NP-complete problems and other second-order concepts; and b) we give more general criteria for checking the first-orderness of an IF sentence.

math.LO↗

arXiv2019

Some observations about generalized quantifiers in logics of imperfect information

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher-order definition of team quantifier. We show that Engström's definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström's quantifiers only range over the latter. We further argue that Engström's definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström's quantifiers.

math.LO↗

arXiv2019

Interventionist Counterfactuals on Causal Teams

We introduce an extension of team semantics which provides a framework for the logic of manipulationist theories of causation based on structural equation models, such as Woodward's and Pearl's; our causal teams incorporate (partial or total) information about functional dependencies that are invariant under interventions. We give a unified treatment of observational and causal aspects of causal models by isolating two operators on causal teams which correspond, respectively, to conditioning and to interventionist counterfactual implication. We then introduce formal languages for deterministic and probabilistic causal discourse, and show how various notions of cause (e.g. direct and total causes) may be defined in them. Through the tuning of various constraints on structural equations (recursivity, existence and uniqueness of solutions, full or partial definition of the functions), our framework can capture different causal models. We give an overview of the inferential aspects of the recursive, fully defined case; and we dedicate some attention to the recursive, partially defined case, which involves a shift of attention towards nonclassical truth values.

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arXiv2018

Team semantics for interventionist counterfactuals and causal dependence

We introduce a generalization of team semantics which provides a framework for manipulationist theories of causation based on structural equation models, such as Woodward's and Pearl's; our causal teams incorporate (partial or total) information about functional dependencies that are invariant under interventions. We give a unified treatment of observational and causal aspects of causal models by isolating two operators on causal teams which correspond, respectively, to conditioning and to interventionist counterfactual implication. The evaluation of counterfactuals may involve the production of partially determined teams. We suggest a way of dealing with such cases by 1) the introduction of formal entries in causal teams, and 2) the introduction of weaker truth values (falsifiability and admissibility), for which we suggest some plausible semantical clauses. We introduce formal languages for both deterministic and probabilistic causal discourse, and study in some detail their inferential aspects. Finally, we apply our framework to the analysis of direct and total causation, and other notions of dependence and invariance.

math.LO↗

arXiv2012

On existential declarations of independence in IF Logic

We analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of IF sentences; we give a syntactical criterion for deciding whether a sentence beginning with such prefix exists such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences. The main theorem allows us to describe the behaviour of various particular classes of quantifier prefixes, and to prove as a remarkable corollary that all existential IF sentences are equivalent to first-order sentences. As a further consequence, we prove that the fragment of IF sentences with knowledge memory has only first-order expressive power (up to truth equivalence).

math.LO↗