Related papers: A Semantic Without Syntax 1
"[M]athematicians care no more for logic than logicians for mathematics." Augustus de Morgan, 1868. Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (1) the Pragmatic Oddity problem must be solved within a general logical treatment of CTD…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
Traditionally, Epistemic Logic represents epistemic scenarios using a single model. This, however, covers only complete descriptions that specify truth values of all assertions. Indeed, many -- and perhaps most -- epistemic descriptions are…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
The halting problem is considered to be an essential part of the theoretical background to computing. That halting is not in general computable has supposedly been proved in many text books and taught on many computer science courses, in…
Recently there has been much interest and progress in extending the definition of contextuality to systems with disturbance. We prove that such an endeavor cannot simultaneously satisfy the following principles: (1) any deterministic system…
This draft introduces the technical machinery of a semantic framework for potentialist truthmaking based on our innovation of intentic states, which are structured partial models accounting for our distinction between non-hypothetical and…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…
Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…
The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over…