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Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal…
In this paper we consider a sufficiently broad class of nonlinear mathematical programs with disjunctive constraints, which, e.g., include mathematical programs with complemetarity/vanishing constraints. We present an extension of the…
We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
Causal Models are increasingly suggested as a means to reason about the behavior of cyber-physical systems in socio-technical contexts. They allow us to analyze courses of events and reason about possible alternatives. Until now, however,…
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion paper. Essentially, an explanation is a…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…
There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…
As large language models (LLMs) witness increasing deployment in complex, high-stakes decision-making scenarios, it becomes imperative to ground their reasoning in causality rather than spurious correlations. However, strong performance on…
In programming models with a reversible semantics, computational steps can be undone. This paper addresses the integration of reversible semantics into process languages for communication-centric systems equipped with behavioral types. In…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
In many real-life settings, agents must navigate dynamic environments while reasoning under incomplete information and acting on a corpus of unstable, context-dependent, and often conflicting norms. We introduce a general, non-modal,…
Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…
Background: Symbolic models, particularly decision trees, are widely used in software engineering for explainable analytics in defect prediction, configuration tuning, and software quality assessment. Most of these models rely on…
Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding -- to the…