Related papers: A general proof system for logics of imperfect inf…
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…
Mathematical proofs should be paired with formal proofs, whenever feasible.
We investigate the completeness of intuitionistic logic with respect to Prawitz's proof-theoretic validity. As an intuitionistic natural deduction system, we apply atomic second-order intuitionistic propositional logic. By developing phase…
We obtain modal completeness of the interpretability logics ILP_0 and ILR w.r.t. generalized Veltman semantics. Our proofs are based on the notion of smart (full) labels. We also give shorter proofs of completeness w.r.t. generalized…
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…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
We propose a large language model explainability technique for obtaining faithful natural language explanations by grounding the explanations in a reasoning process. When converted to a sequence of tokens, the outputs of the reasoning…
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…