Related papers: Representation Theorems for Cumulative Proposition…
Suppose we want to build a system that answers a natural language question by representing its semantics as a logical form and computing the answer given a structured database of facts. The core part of such a system is the semantic parser…
In everyday life it happens that a person has to reason about what other people think and how they behave, in order to achieve his goals. In other words, an individual may be required to adapt his behaviour by reasoning about the others'…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence. In an influential paper, Valiant recognised that the challenge of learning should be…
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…
We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice…
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…
Several authors have recently defined intuitionistic logic based on team semantics (tIPC). In this paper we provide two alternative approaches to intermediate logics in the team semantics setting. We do this by modifying tIPC with axioms…
This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
In a number of papers, Y. Sternfeld investigated the problems of representation of continuous and bounded functions by linear superpositions. In particular, he proved that if such representation holds for continuous functions, then it holds…