Related papers: Dialectica Logical Principles
Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
Recent years have witnessed the emergence of a variety of post-hoc interpretations that aim to uncover how natural language processing (NLP) models make predictions. Despite the surge of new interpretation methods, it remains an open…
This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In…
Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped…
This thesis is concerned with type-logical grammars and their practical applicability as tools of reasoning about sentence syntax and semantics. The focal point is narrowed to Dutch, a language exhibiting a large degree of word order…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Recently, data abstraction has been studied in the context of separation logic, with noticeable practical successes: the developed logics have enabled clean proofs of tricky challenging programs, such as subject-observer patterns, and they…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
We suggest an ordering for the predicates in continuous logic so that the semantics of continuous logic can be formulated as a hyperdoctrine. We show that this hyperdoctrine can be embedded into the hyperdoctrine of subobjects of a suitable…
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,…
The Aristotelian syllogistic cannot account for the validity of many inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a)…
The minimum classical extension S$^{+g}$ of a classically sound theory S based on intuitionistic logic, defined by adding to S the Gentzen negative interpretations of its mathematical axioms, contains a faithful translation S$^g$ of the…
We introduce a new application for inductive logic programming: learning the semantics of programming languages from example evaluations. In this short paper, we explored a simplified task in this domain using the Metagol meta-interpretive…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…