Related papers: A new decision method for Intuitionistic Logic by …
In 1988, Ivlev proposed four-valued non-deterministic semantics for modal logics in which the alethic T axiom holds good. Unfortunately, no completeness was proved. In previous work, we proved completeness for some Ivlev systems and…
The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and…
We present a hierarchical framework for analysing propositional linear-time temporal logic (PTL) to obtain standard results such as a small model property, decision procedures and axiomatic completeness. Both finite time and infinite time…
We study an intuitionistic version of common knowledge logic (CK), called ICK, which was introduced by J\"ager and Marti. ICK extends intuitionistic propositional logic (IPL) by multiple box modalities interpreted as knowledge operators for…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
We reformulate Pratt's tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and more direct for implementation. Extending the method we give the first EXPTIME (optimal) tableau…
Inductive Logic Programming (ILP) combines rule-based and statistical artificial intelligence methods, by learning a hypothesis comprising a set of rules given background knowledge and constraints for the search space. We focus on extending…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently,…
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…
Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…
When modeling real world domains we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we…
We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
We give an optimal (EXPTIME), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound…
Vision-language models such as CLIP achieve strong visual-textual alignment, but often suffer from overfitting and limited interpretability when adapted through continuous prompt learning. While discrete prompt optimization improves…