Related papers: Logical Varieties in Normative Reasoning
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
In this paper, we study logics of dependence on the propositional level. We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well…
A logic family is a bunch of logics that belong together in some way. First-order logic is one of the examples. Logics organized into a structure occurs in abstract model theory, institution theory and in algebraic logic. Logic families…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
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…
The reasoning abilities of large language models (LLMs) are the topic of a growing body of research in AI and cognitive science. In this paper, we probe the extent to which twenty-nine LLMs are able to distinguish logically correct…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification…
We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…
It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
Stereotypical reasoning assumes that the situation at hand is one of a kind and that it enjoys the properties generally associated with that kind of situation. It is one of the most basic forms of nonmonotonic reasoning. A formal model for…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Large language models (LLMs) have achieved remarkable successes on various tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs, which can be categorized into the…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…