Related papers: A Proof of Stavi's Theorem
What are the most general principles in set theory relating forceability and truth? As with Solovay's celebrated analysis of provability, both this question and its answer are naturally formulated with modal logic. We aim to do for…
In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABBar for short), interpreted over natural numbers. We first introduce the logic and we show that it is…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
Provability logic concerns the study of modality $\Box$ as provability in formal systems such as Peano arithmetic. Natural, albeit quite surprising, topological interpretation of provability logic has been found in the 1970's by Harold…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…
A temporal logic is presented for reasoning about the correctness of timed concurrent constraint programs. The logic is based on modalities which allow one to specify what a process produces as a reaction to what its environment inputs.…
In these notes we propose a new, simpler proof system for first-order matching logic with application and definedness. The new proof system is inspired by Tarski's axiomatization for first order-logic with equality (simplified by Kalish and…
We introduce Temporal Ensemble Logic (TEL), a monadic, first-order modal logic for linear-time temporal reasoning. TEL includes primitive temporal constructs such as ``always up to $t$ time later'' ($\Box_t$), ``sometimes before $t$ time in…
It is well known that (timed) $\omega$-regular properties such as `p holds at every even position' and `p occurs at least three times within the next 10 time units' cannot be expressed in Metric Interval Temporal Logic ($\mathsf{MITL}$) and…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist…
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
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…
In this paper, we prove a version of the typed B\"ohm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a…
In this paper, we introduce a general family of sequent-style calculi over the modal language and its fragments to capture the essence of all constructively acceptable systems. Calling these calculi \emph{constructive}, we show that any…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable assignments. Unlike in the…