Related papers: Axiomatic Aspects of Default Inference
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
I explore the relationships between Prawitz's approach to non-monotonic proof-theoretic validity, which I call reducibility semantics, and some later proof-theoretic approaches, which I call standard base semantics and Sandqvist's base…
In this paper, we provide more evidence for the contention that logical consequence should be understood in normative terms. Hartry Field and John MacFarlane covered the classical case. We extend their work, examining what it means for an…
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
We develop a design-based framework for causal inference that accommodates random potential outcomes without introducing outcome models, thereby extending the classical Neyman--Rubin paradigm in which outcomes are treated as fixed. By…
Adaptive designs dynamically update treatment probabilities using information accumulated during the experiment. Existing theory for causal inference from adaptive experiments primarily assumes the superpopulation framework with independent…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
We study the interaction of views, queries, and background knowledge in the form of existential rules. The motivating questions concern monotonic determinacy of a query using views w.r.t. rules, which refers to the ability to recover the…
This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of…
Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different…
When speaking or writing, people omit information that seems clear and evident, such that only part of the message is expressed in words. Especially in argumentative texts it is very common that (important) parts of the argument are implied…
I discuss two approaches to monotonic proof-theoretic semantics. In the first one, which I call SVA, consequence is understood in terms of existence of valid arguments. The latter involve the notions of argument structure and justification…
Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. While the usual implication (i.e., the neck of a Horn clause) stands for…
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…
We investigate properties of ABA+, a formalism that extends the well studied structured argumentation formalism Assumption-Based Argumentation (ABA) with a preference handling mechanism. In particular, we establish desirable properties that…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals). The notion of qualitative change of view that thus arises is…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…