diff --git a/argus/src/parser/lexer.rs b/argus/src/parser/lexer.rs
index 56ba8ff..1caf017 100644
--- a/argus/src/parser/lexer.rs
+++ b/argus/src/parser/lexer.rs
@@ -139,8 +139,8 @@ pub fn lexer<'src>() -> impl Parser<'src, &'src str, Output<'src>, Error<'src>>
         just("&&").to(Token::And),
         just("&").to(Token::And),
         just("\u{2227}").to(Token::And), // ∧
-        just("||").to(Token::And),
-        just("|").to(Token::And),
+        just("||").to(Token::Or),
+        just("|").to(Token::Or),
         just("\u{2228}").to(Token::Or), // ∨
         just("^").to(Token::Xor),
         just("-").to(Token::Minus),
diff --git a/argus/src/parser/mod.rs b/argus/src/parser/mod.rs
index bd9450b..c8c76ac 100644
--- a/argus/src/parser/mod.rs
+++ b/argus/src/parser/mod.rs
@@ -7,6 +7,7 @@ mod lexer;
 mod syntax;
 
 use chumsky::prelude::Rich;
+use itertools::Itertools;
 use lexer::{lexer, Token};
 use syntax::{parser, Expr, Interval};
 
@@ -17,6 +18,10 @@ pub fn parse_str(src: &str) -> Result<crate::core::expr::Expr, Vec<Rich<'_, Stri
     use chumsky::prelude::{Input, Parser};
 
     let (tokens, lex_errors) = lexer().parse(src).into_output_errors();
+    log::debug!("** Tokens output **");
+    log::debug!("{:#?}", tokens);
+    log::debug!("** Lexing Errors **");
+    log::debug!("[{}]", lex_errors.iter().map(|e| e.to_string()).join("\n- "));
 
     let (parsed, parse_errors) = if let Some(tokens) = &tokens {
         parser()
@@ -26,6 +31,11 @@ pub fn parse_str(src: &str) -> Result<crate::core::expr::Expr, Vec<Rich<'_, Stri
         (None, Vec::new())
     };
 
+    log::debug!("** Parse output **");
+    log::debug!("{:#?}", parsed);
+    log::debug!("** Parse Errors **");
+    log::debug!("[{}]", parse_errors.iter().map(|e| e.to_string()).join("\n- "));
+
     let (expr, expr_errors) = if let Some((ast, span)) = parsed {
         let mut expr_builder = ExprBuilder::new();
         let result = ast_to_expr(&ast, span, &mut expr_builder);
@@ -37,6 +47,11 @@ pub fn parse_str(src: &str) -> Result<crate::core::expr::Expr, Vec<Rich<'_, Stri
         (None, vec![])
     };
 
+    log::debug!("** Final Expression **");
+    log::debug!("{:#?}", expr);
+    log::debug!("** AST to Expr Errors **");
+    log::debug!("[{}]", expr_errors.iter().map(|e| e.to_string()).join("\n- "));
+
     let errors: Vec<_> = lex_errors
         .into_iter()
         .map(|e| e.map_token(|c| c.to_string()))
diff --git a/argus/src/parser/syntax.rs b/argus/src/parser/syntax.rs
index 8be5990..f00e78b 100644
--- a/argus/src/parser/syntax.rs
+++ b/argus/src/parser/syntax.rs
@@ -21,12 +21,21 @@ pub enum UnaryOps {
 }
 
 impl UnaryOps {
+    /// Get the default type for the *arguments* of this kind of expression.
     fn default_args_type(&self) -> Type {
         match self {
             UnaryOps::Neg => Type::Float,
             _ => Type::Bool,
         }
     }
+
+    /// Get the default type the expression with this operator should be
+    fn get_default_type(&self) -> Type {
+        match self {
+            UnaryOps::Neg => Type::Float,
+            _ => Type::Bool,
+        }
+    }
 }
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
@@ -50,6 +59,7 @@ pub enum BinaryOps {
 }
 
 impl BinaryOps {
+    /// Get the default type for the *arguments* of this kind of expression.
     fn default_args_type(&self) -> Type {
         match self {
             BinaryOps::Add
@@ -65,6 +75,14 @@ impl BinaryOps {
             _ => Type::Bool,
         }
     }
+
+    /// Get the default type the expression with this operator should be
+    fn get_default_type(&self) -> Type {
+        match self {
+            BinaryOps::Add | BinaryOps::Sub | BinaryOps::Mul | BinaryOps::Div => Type::Float,
+            _ => Type::Bool,
+        }
+    }
 }
 
 #[derive(Debug, Clone, PartialEq)]
@@ -103,12 +121,12 @@ impl<'src> Expr<'src> {
                 op,
                 interval: _,
                 arg: _,
-            } => op.default_args_type(),
+            } => op.get_default_type(),
             Expr::Binary {
                 op,
                 interval: _,
                 args: _,
-            } => op.default_args_type(),
+            } => op.get_default_type(),
         }
     }
 
@@ -174,7 +192,7 @@ fn num_expr_parser<'tokens, 'src: 'tokens>(
 
         let num_atom = var
             .or(num_literal)
-            .map_with(|expr, e| (expr, e.span()))
+            .map_with(|e, ctx| (e, ctx.span()))
             // Atoms can also just be normal expressions, but surrounded with parentheses
             .or(num_expr.clone().delimited_by(just(Token::LParen), just(Token::RParen)))
             // Attempt to recover anything that looks like a parenthesised expression but contains errors
@@ -297,39 +315,36 @@ pub(crate) fn parser<'tokens, 'src: 'tokens>(
                 [],
                 |span| (Expr::Error, span),
             )))
-            .or(expr)
             .boxed();
 
-        let not_op = just(Token::Not)
-            .map_with(|_, e| (UnaryOps::Not, e.span()))
-            .repeated()
-            .foldr(atom, |op, rhs| {
-                let span = op.1.start..rhs.1.end;
-                (Expr::unary_op(op.0, rhs, None), span.into())
-            })
-            .boxed();
-
-        let unary_temporal_op = {
+        let unary_op = {
             let op = choice((
+                just(Token::Not).to(UnaryOps::Not),
                 just(Token::Next).to(UnaryOps::Next),
                 just(Token::Eventually).to(UnaryOps::Eventually),
                 just(Token::Always).to(UnaryOps::Always),
             ));
             op.map_with(|op, e| (op, e.span()))
                 .then(interval.clone().or_not())
+                .try_map(|(op, interval), _| match (op, interval) {
+                    ((UnaryOps::Not, _), Some((_, s))) => {
+                        Err(Rich::custom(s, "Not (`!`) operator cannot have an interval"))
+                    }
+                    (o, i) => Ok((o, i)),
+                })
                 .repeated()
-                .foldr(not_op, |(op, interval), rhs| {
+                .foldr(atom, |(op, interval), rhs| {
                     let span = op.1.start..rhs.1.end;
                     (Expr::unary_op(op.0, rhs, interval), span.into())
                 })
                 .boxed()
         };
 
-        let binary_temporal_op = unary_temporal_op
+        let until_op = unary_op
             .clone()
             .then(just(Token::Until).to(BinaryOps::Until).then(interval.or_not()))
             .repeated()
-            .foldr(unary_temporal_op, |(lhs, (op, interval)), rhs| {
+            .foldr(unary_op, |(lhs, (op, interval)), rhs| {
                 let span = lhs.1.start..rhs.1.end;
                 assert_eq!(op, BinaryOps::Until);
                 (Expr::binary_op(op, (lhs, rhs), interval), span.into())
@@ -338,9 +353,9 @@ pub(crate) fn parser<'tokens, 'src: 'tokens>(
 
         let and_op = {
             let op = just(Token::And).to(BinaryOps::And);
-            binary_temporal_op
+            until_op
                 .clone()
-                .foldl(op.then(binary_temporal_op).repeated(), |a, (op, b)| {
+                .foldl(op.then(until_op).repeated(), |a, (op, b)| {
                     let span = a.1.start..b.1.end;
                     (Expr::binary_op(op, (a, b), None), span.into())
                 })