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# Questions tagged [lo.logic]

Computational and mathematical logic.

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### To what extent MSO = WS1S, when adding relations?

[This question has been asked on MathOverflow with no luck a month ago.] Let me first clarify my definitions. For a word $w \in \Sigma^*$, with $\Sigma =\{a_1, \ldots, a_n\}$, I define two ...
344 views

### Descriptive complexity of communication complexity classes

It is well known that some major complexity classes, like P or NP, admit a full logical characterization (e.g NP = existential 2nd order logic by Fagin's theorem). On the other hand, one can also ...
164 views

### Counting solutions to extended MSO formulas, and sampling — do these appear in the literature?

I am trying to determine if the literature contains various extensions of Courcelle's theorem. Since I haven't been able to find these in the literature, I guess that these are folklore results, or ...
290 views

### Proof assistant formalizations of Finite Model Theory

I'm wondering if anyone knows of a formalization (even limited) of any part of finite model theory in any of the major proof assistants. (I'm most familiar with Coq, but Isabelle, Agda, etc. would ...
160 views

### Is the theory of asymptotic bounds finitely axiomatizable?

Let $F$ be the set of functions over real numbers. Consider the structure $M = \langle F, <, \leq, =, \geq, > \rangle$ where the $<, \leq, =, \geq, >$ are defined as asymptotic notions $o$...
216 views

### Combinator logic and unification

Summary: if we are trying to use combinator logic to solve first-order logic type problems, is the best method to feed in free variables and use the standard first-order unification algorithm? In ...
199 views

### Categorical semantics for S5 modal logic?

Does anyone know where I can look to find out what the generally categorical semantics of S5 is? For S4, the answer is well-known: we want a Cartesian closed category with a product-preserving ...
171 views

I have found the following question at openproblemgarden.org: The problem concerns the extension of Monadic Second Order Logic (over a binary relation representing the edge relation) with the ...
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90 views

### Looking for a specific tree automata model

is there any tree automata model over unranked trees (that is with unbounded number of children for each node), such that: Checking non-emptiness and universality is decidable in elementary time, ...
125 views

### Family of formulas for which Gabbay's separation algorithm explodes nonelementarily

It is repeated throughout the literature that Gabbay's algorithm for separation of LTL with Since and Until can produce nonelementary blow-up of the size of the formula, but I have never seen a proof ...
128 views

### Efficiently computing the union of all minimal unsatisfiable constraint sets in a first-order unification problem

Suppose we are given a standard first-order unification problem, represented as a set $D$ of term equality constraints, such that the system $D$ as a whole is unsatisfiable. Consider the minimal ...
129 views

### Evaluating boolean formula without knowing all values

I am looking for research approaches for the following problem: assume we have a set of $m$ computers, each carries a bit, and a Boolean formula $\varphi$ over those $m$ variables. The computers are ...
95 views

### How to develop an effective notation for a partially ordered logic?

I am developing a logic for reasoning about programs in a resource-constrained environment. My starting point is intuitionistic linear logic, but I made the following changes: In intuitionistic ...
106 views

### When can an inner existential quantifier be eliminated in favour of a function relating terms?

I have a question which somehow relates to the great answer by Bauer in the question Techniques for Reversing the Order of Quantiﬁers, where he discusses how the possibility of quantifier reversing ...
120 views

### Expansion normal forms of confluent term rewriting systems

Suppose one has two rewrite rules $\to^\eta,\to^\beta$, both of which are confluent and such that $\to^A := \to^{(\eta \cup \beta)}$ is also confluent. Define a $\beta$-normal form relative to $\eta$ ...
129 views

### How do computers check if two functions are the same?

To prove that two given functions are the same involves proving infinitely many statements. I wonder how to implement so that a computer can check such a statement? An easy example is the following: ...
86 views

### Forward chaining algorithms

I am interested in learning about the current state of the art regarding forward chaining production systems. I understand that things haven't changed much (regarding the basic algorithms) since 1995'...
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### Notion of “quotient” or “inverse” for recognizable tree languages?

Related to my previous question but this time I have a better idea of what I'm actually asking. I'm looking at the following operation on recognizable tree languages (i.e. regular tree grammars, ...
44 views

### Is there a complete and finite axiom scheme for conditional independence? (Graphoids)

Note: This is a better-written version of an unanswered question asked before on MathOverflow. Question: Is there a complete and finite axiom scheme for conditional probability? If so, is ...
57 views

### Decidability of the monadic second-order theory of a class of finite structures

Let $L$ be the set of sentences in some logic. I am interested in cases where $L$ is the set of sentences in monadic second-order logic, or it is its $\Pi^1_1$ fragment. Let $K$ be a class of finite ...
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### Applications of the monoidal closed structure in LTL?

A simple model of temporal logic is via time-indexed truth functions. This lets us model the Boolean connectives, as well as the next-step operator and modal always operator:  \begin{array}{lclll} ...
I have a simple constraint system with a finite set $C$ of constant symbols, an infinite set $V$ of variables, and two relation symbols - $R_1$, a preorder, and $R_2$, an equivalence relation. ...