Related papers: A Constructive Epistemic Logic with Public Announc…

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…

Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…

Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…

We present a resolution of the celebrated "Surprise Exam Paradox". We argue that if the surprise exam story is analyzed using the exact same meaning of the notion of "surprise" as is dictated by the story itself, then no paradox arises.

We derive a Prolog theorem prover for an Intuitionistic Epistemic Logic by starting from the sequent calculus {\bf G4IP} that we extend with operator definitions providing an embedding in intuitionistic propositional logic ({\bf IPC}). With…

We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

The 'expected utility hypothesis' and 'Savage's Sure-Thing Principle' are violated in real life decisions, as shown by the 'Allais' and 'Ellsberg paradoxes'. The popular explanation in terms of 'ambiguity aversion' is not completely…

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…

In Probabilistic Logic Nilsson uses the device of a probability distribution over a set of possible worlds to assign probabilities to the sentences of a logical language. In his paper Nilsson concentrated on inference and associated…

This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…

In game theory, the notion of a player's beliefs about the game players' beliefs about other players' beliefs arises naturally. In this paper, we present a non-self-referential paradox in epistemic game theory which shows that completely…

We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial 'bang' correlates all events, just as in the superdeterministic universe. We introduce the…

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from…

Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…

In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…

In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted,…

Counterfactual explanations (CEs) are a practical tool for demonstrating why machine learning classifiers make particular decisions. For CEs to be useful, it is important that they are easy for users to interpret. Existing methods for…

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…